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Chapter 7: Factoring

7.9 Age Word Problems

One application of linear equations is what are termed age problems. When solving age problems, generally the age of two different people (or objects) both now and in the future (or past) are compared. The objective of these problems is usually to find each subject’s current age. Since there can be a lot of information in these problems, a chart can be used to help organize and solve. An example of such a table is below.

Example 7.9.1

Joey is 20 years younger than Becky. In two years, Becky will be twice as old as Joey. Fill in the age problem chart, but do not solve.

  • The first sentence tells us that Joey is 20 years younger than Becky (this is the current age)
  • The age change for both Joey and Becky is plus two years
  • In two years, Becky will be twice the age of Joey in two years

Using this last statement gives us the equation to solve:

B + 2 = 2 ( B − 18)

Example 7.9.2

Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?

  • The first sentence tells us that Carmen is 12 years older than David (this is the current age)
  • The second sentence tells us the age change for both Carmen and David is five years ago (−5)

Filling in the chart gives us:

The last statement gives us the equation to solve:

Five years ago, the sum of their ages was 28

[latex]\begin{array}{rrrrrrrrl} (D&+&7)&+&(D&-&5)&=&28 \\ &&&&2D&+&2&=&28 \\ &&&&&-&2&&-2 \\ \hline &&&&&&2D&=&26 \\ \\ &&&&&&D&=&\dfrac{26}{2} = 13 \\ \end{array}[/latex]

Therefore, Carmen is David’s age (13) + 12 years = 25 years old.

Example 7.9.3

The sum of the ages of Nicole and Kristin is 32. In two years, Nicole will be three times as old as Kristin. How old are they now?

  • The first sentence tells us that the sum of the ages of Nicole (N) and Kristin (K) is 32. So N + K = 32, which means that N = 32 − K or K = 32 − N (we will use these equations to eliminate one variable in our final equation)
  • The second sentence tells us that the age change for both Nicole and Kristen is in two years (+2)

In two years, Nicole will be three times as old as Kristin

[latex]\begin{array}{rrrrrrr} N&+&2&=&3(34&-&N) \\ N&+&2&=&102&-&3N \\ +3N&-&2&&-2&+&3N \\ \hline &&4N&=&100&& \\ \\ &&N&=&\dfrac{100}{4}&=&25 \\ \end{array}[/latex]

If Nicole is 25 years old, then Kristin is 32 − 25 = 7 years old.

Example 7.9.4

Louise is 26 years old. Her daughter Carmen is 4 years old. In how many years will Louise be double her daughter’s age?

  • The first sentence tells us that Louise is 26 years old and her daughter is 4 years old
  • The second line tells us that the age change for both Carmen and Louise is to be calculated ([latex]x[/latex])

In how many years will Louise be double her daughter’s age?

[latex]\begin{array}{rrrrrrr} 26&+&x&=&2(4&+&x) \\ 26&+&x&=&8&+&2x \\ -26&-&2x&&-26&-&2x \\ \hline &&-x&=&-18&& \\ &&x&=&18&& \end{array}[/latex]

In 18 years, Louise will be twice the age of her daughter.

For Questions 1 to 8, write the equation(s) that define the relationship.

  • Rick is 10 years older than his brother Jeff. In 4 years, Rick will be twice as old as Jeff.
  • A father is 4 times as old as his son. In 20 years, the father will be twice as old as his son.
  • Pat is 20 years older than his son James. In two years, Pat will be twice as old as James.
  • Diane is 23 years older than her daughter Amy. In 6 years, Diane will be twice as old as Amy.
  • Fred is 4 years older than Barney. Five years ago, the sum of their ages was 48.
  • John is four times as old as Martha. Five years ago, the sum of their ages was 50.
  • Tim is 5 years older than JoAnn. Six years from now, the sum of their ages will be 79.
  • Jack is twice as old as Lacy. In three years, the sum of their ages will be 54.

Solve Questions 9 to 20.

  • The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary.
  • The sum of the ages of a father and son is 56. Four years ago, the father was 3 times as old as the son.
  • The sum of the ages of a wood plaque and a bronze plaque is 20 years. Four years ago, the bronze plaque was one-half the age of the wood plaque.
  • A man is 36 years old and his daughter is 3. In how many years will the man be 4 times as old as his daughter?
  • Bob’s age is twice that of Barry’s. Five years ago, Bob was three times older than Barry. Find the age of both.
  • A pitcher is 30 years old, and a vase is 22 years old. How many years ago was the pitcher twice as old as the vase?
  • Marge is twice as old as Consuelo. The sum of their ages seven years ago was 13. How old are they now?
  • The sum of Jason and Mandy’s ages is 35. Ten years ago, Jason was double Mandy’s age. How old are they now?
  • A silver coin is 28 years older than a bronze coin. In 6 years, the silver coin will be twice as old as the bronze coin. Find the present age of each coin.
  • The sum of Clyde and Wendy’s ages is 64. In four years, Wendy will be three times as old as Clyde. How old are they now?
  • A sofa is 12 years old and a table is 36 years old. In how many years will the table be twice as old as the sofa?
  • A father is three times as old as his son, and his daughter is 3 years younger than his son. If the sum of all three ages 3 years ago was 63 years, find the present age of the father.

Answer Key 7.9

Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Here are some examples for calculating age in word problems.

Phil is Tom's father. Phil is 35 years old. Three years ago, Phil was four times as old as his son was then. How old is Tom now?

First, circle what it is you must ultimately find— how old is Tom now? Therefore, let t be Tom's age now. Then three years ago, Tom's age would be t – 3. Four times Tom's age three years ago would be 4( t – 3). Phil's age three years ago would be 35 – 3 = 32. A simple chart may also be helpful.

Now, use the problem to set up an equation.

to solve age problems

Therefore, Tom is now 11.

Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa?

First, circle what you must find— how old is Lisa? Let Lisa equal x . Therefore, Kathy is x + 16. (Note that since Lisa is 16 years younger than Kathy, you must add 16 years to Lisa to denote Kathy's age.) Now, use the problem to set up an equation.

to solve age problems

Therefore, Lisa is 7 years old.

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"Age" Word Problems

Age Probs Diophantus

What are "age" word problems?

"Age" type word problems are those which compare two persons' ages, or one person's ages at different times in their lives, or some combination thereof.

Here's an example from my own life:

Content Continues Below

Age Word Problems on MathHelp.com

Age Word Problems

  • In January of the year 2000, I was one more than eleven times as old as my son Will. In January of 2009, I was seven more than three times as old as him. How old was my son in January of 2000?

Obviously, in "real life" you'd have walked up to my kid and asked him how old he was, and he'd have proudly held up three grubby fingers, but that won't help you on your homework.

Here's how you'd figure out his age, if you'd been asked the above question in your math class:

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First, I'll need to name things and translate the English into math.

Since my age was defined in terms of Will's, I'll start with a variable for Will's age. To make it easy for me to remember the meaning of the variable, I will pick W to stand for "Will's age at the start, in the year 2000". Then Will's age in 2009, being nine years later, will be W + 9 . So I have the following information:

Will's age in 2000: W

Will's age in 2009: W + 9

My age was defined in terms of the above expressions. In the year 2000, I was "eleven times Will's age in the year 2000, plus one more", giving me:

my age in 2000: 11(W) + 1

My age in 2009 was also defined in terms of Will's age in 2009. Specifically, I was "three times Will's age in 2009, plus seven more", giving me:

my age in 2009: 3(W + 9) + 7

But I was also nine years older than I had been in the year 2000, which gives me another expression for my age in 2009:

my age in 2009: [ 11(W) + 1 ] + 9

My age in 2009 was my age in 2009. This fact means that the two expressions for "my age in 2009" must represent the same value. And this fact, in turn, allows me to create an equation — by setting the two equal-value expressions equal to each other:

3(W + 9) + 7 = [11(W) + 1] + 9

Solving, I get:

3W + 27 + 7 = 11W + 1 + 9

3W + 34 = 11W + 10

34 = 8W + 10

Since I set up this equation using expressions for my age, it's tempting to think that 3 = W stands for my age. But this is why I picked W to stand for "Will's age"; the variable reminds me that, no, 3 = W stands for Will's age, not mine.

And this is exactly what the question had asked in the first place. How old was Will in the year 2000?

Will was three years old.

Note that this word problem did not ask for the value of a variable; it asked for the age of a person. So a properly-written answer reflects this. " W = 3 " would not be an ideal response.

What are the steps for solving an age-based word problem?

The important steps for solving an age-based word problem are as follows:

  • Figure out what is defined in terms of something else
  • Set up a variable for that "something else" (labelling it clearly with its definition)
  • Create an expression for the first time frame, and then
  • Increment the expressions by the required amount (in the example above, this increment was nine years) to reflect the passage of time.

Don't try to use the same variable or expression to stand for two different things! Since, in the above, W stands for Will's age in 2000, then W can not also stand for his age in 2009. Make sure that you are very explicit about this when you set up your variables, expressions, and equations; write down the two sets of information as two distinct situations.

  • Currently, Andrei is three times Nicolas' age. In ten years, Andrei will be twelve years older than Nicolas. What are their ages now?

Andrei's age in defined in terms of Nicolas' age, so I'll pick a variable for Nicolas' age now; say, " N ". This allows me to create an expression for Andrei's age now, which is three times that of Nicolas.

Nicolas' age now: N

Andrei's age now: 3N

In ten years, they each will be ten years older, so I'll add 10 to each of the above for their later ages.

Nicolas' age later: N + 10

Andrei's age later: 3N + 10

But I am also given that, in ten years, Andrei will be twelve years older than Nicolas. So I can create another expression for Andrei's age in ten years; namely, I'll take the expression for Nicolas' age in ten years, and add twelve to that.

Andrei's age later: [N + 10] + 12

Since Andrei's future age will equal his future age, I can take these two expressions for his future age, set them equal (thus creating an equation), and solve for the value of the variable.

3N + 10 = [N + 10] + 12

3N + 10 = N + 22

2N + 10 = 22

Okay; I've found the value of the variable. But, looking back at the original question, I see that they're wanting to know the current ages of two people. The variable stands for the age of the younger of the two. Since the older is three times this age, then the older is 18 years old. So my clearly-stated answer is:

Nicolas is 6 years old.

Andrei is 18 years old.

  • One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

This problem refers to Heather's age two years into the future and three years back in the past. Unlike most "age" word problems, this exercise is not comparing two different people's ages at the same point in time, but rather the same person's ages at different points in time.

They ask for Heather's age now, so I'll pick a variable to stand for this unknown; say, H . Then I'll increment this variable in order to create expressions for "two years ago" and "two years from now".

age two years from now: H + 2

age three years ago: H − 3

Now I need to create expressions, using the above, which will stand for certain fractions of these ages:

The sum of these two expressions is given as being " 20 ", so I'll add the two expressions, set their sum equal to 20 , and solve for the variable:

H / 2 + 1 + H / 3 − 1 = 20 H / 2 + H / 3 = 20 3H + 2H = 120 5H = 120 H = 24

Okay; I've found the value of the variable. Now I'll go back and check my definition of that variable (so I see that it stands for Heather's current age), and I'll check for what the exercise actually asked me to find (which was Heather's current age). So my answer is:

Heather is 24 years old.

Note: Remember that you can always check your answer to any "solving" exercise by plugging that answer back into the original problem. In the case of the above exercise, if Heather is 24 now, then she will be 26 in two years, half of which is 13 ; three years ago, she would have been 21 , a third of which is 7 . Adding, I get 13 + 7 = 20 , so my solution checks.

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  • In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68 . How old is each one now?

The grandfather's age is defined in terms of Miguel's age, so I'll pick a variable to stand for Miguel's age. Since they're asking me for current ages, my variable will stand for Miguel's current age.

Miguel's age now: m

Now I'll use this variable to create expressions for the various items listed in the exercise.

Miguel's age last year: m − 1

six times Miguel's age last year: 6( m − 1)

Miguel's grandfather's age will, in another three years, be six times what Miguel's age was last year. This means that his grandfather is currently three years less than six times Miguel's age from last year, so:

grandfather's age now: 6( m − 1) − 3

Summing the expressions for the two current ages, and solving, I get:

( m ) + [6( m − 1) − 3] = 68

m + [6 m − 6 − 3] = 68

m + [6 m − 9] = 68

7 m − 9 = 68

Looking back, I see that this variable stands for Miguel's current age, which is eleven. But the exercise asks me for the current ages of bother of them, so:

Last year, Miguel would have been ten. In three more years, his grandfather will be six times ten, or sixty. So his grandfather must currently be 60 −3 = 57 .

Miguel is currently 11 .

His grandfather is currently 57 .

The puzzler on the next page is an old one (as in "Ancient Greece" old), but it keeps cropping up in various forms. It's rather intricate.

URL: https://www.purplemath.com/modules/ageprobs.htm

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Algebra: Age Word Problems

Related Pages Word Problems Involving Age Solving Age Word Problems Using Algebra More Algebra Lessons

Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future.

How To Solve Age Word Problems?

If the problem involves a single person, then it is similar to an Integer Problem. Read the problem carefully to determine the relationship between the numbers. This is shown in the examples involving a single person .

If the age problem involves the ages of two or more people then using a table would be a good idea. A table will help you to organize the information and to write the equations. This is shown in the examples involving more than one person .

How To Solve Age Problems Involving A Single Person?

Example: Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

Solution: Step 1: Let x be John’s age now. Look at the question and put the relevant expressions above it.

Step 2: Write out the equation.

Isolate variable x

Answer: John is now 18 years old.

How To Use Algebra To Solve Age Problems?

  • Ten years from now, Orlando will be three times older than he is today. What is his current age?
  • In 20 years, Kayleen will be four times older than she is today. What is her current age?

How To Solve Age Problems Involving More Than One Person?

Example: John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?

Solution: Step 1 : Set up a table.

Step 2: Fill in the table with information given in the question. John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?

Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.

Write the new relationship in an equation using the ages in 5 yrs.

In 5 years, John will be three times as old as Alice.

2 x + 5 = 3 ( x – 5 + 5) 2 x + 5 = 3 x

Isolate variable x x = 5

Answer: Peter is now 5 years old.

Example: John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

Solution: Step 1: Set up a table.

Step 2: Fill in the table with information given in the question. John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

Let x be John’s age now. Add 2 to get the ages in 2 yrs.

Write the new relationship in an equation using the ages in 2 yrs.

In two years time, the sum of their ages will be 58.

Answer: John is now 8 years old.

How To Solve Word Problems With Multiple Ages?

Example: Ben is eight years older than Sarah. 10 years ago, Ben was twice as old as Sarah. Currently, how old is Ben and Sarah?

Algebra Word Problems With Multiple Ages Example: Mary is three times as old as her son. In 12 years, Mary’s age will be one year less than twice her son’s age. How old is each now?

Algebra Word Problem With Past And Present Ages Example: Arun is 4 times as old as Anusha is today. Sixty years ago, Arun was 6 times as old as Anusha. How old are they today?

Algebra Age Word Problem With Past, Present, And Future Ages How to organize the data using a table and solve using a system of linear equations?

  • Sally is 3 times as old as John. 8 years from now, Sally will be twice as old as John. How old is John?
  • Kim is 6 years more than twice Timothy’s age. 2 years ago, Kim was three times as old as Timothy. How old was Kim 2 years ago?
  • Leah is 2 less than 3 times Rachel’s age. 3 years from now, Leah will be 7 more than twice Rachel’s age. How old will Rachel be in 3 years from now?
  • Becca is twice as old as Susan and Greg is 9 years older than Susan. 3 years ago, Becca was 9 less than 3 times Susan’s age. How old is Greg now?
  • Lauren is 3 less than twice Andrew’s age. 4 years from now, Sam will be 2 more than twice Andrew’s age. 5 years ago, Sam was three times Andrew’s age. How old was Lauren 5 years ago?
  • Gabby is 1 year more than twice Larry’s age. 3 years from now, Megan will be 27 less than twice Gabby’s age. 4 years ago, Megan was 1 year less than 3 times Larry’s age. How old will Megan be 3 years from now?

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Which came first, the Biden age concerns or the coverage of them?

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It is immediately obvious why the White House pushed back as hard as it did on a draft of a report from special counsel Robert Hur summarizing his investigation into President Biden’s possession of classified materials. Hur’s report, both in draft and in its final release , suggested that Biden suffered from significant memory issues, a criticism that was ostensibly offered as a predicate for not filing criminal charges.

In part because the report otherwise offered little grist for discussion, Hur’s elevation of those memory issues has become a focus of news coverage. House Republicans looped his allegations into their ongoing effort to hobble Biden’s reelection chances. The recurring discussion of Biden’s acuity had a new peg — one that generated new criticism of the media’s coverage.

The Hur report’s assessment of Biden immediately brought to mind to many on the left the discussion of Hillary Clinton’s email server in the run-up to the 2016 election. Here again, it seemed, was a (Republican) government official exploring a subject that was politically damaging to a presidential candidate , just like then-FBI Director James B. Comey. And here again was a media willing to hype this issue that Americans wouldn’t otherwise care about.

But this is overly neat. Although there is a valid discussion to be had over the focus on Biden’s age and capacity, those concerns — which are common among voters — are not obviously media-driven.

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That’s not to say it’s entirely organic. One of the first people to draw attention to Biden’s faculties before his 2020 presidential bid was Donald Trump . In early 2018, Trump began referring to Biden as “Sleepy Joe.” (Only recently did he abandon this for “Crooked Joe,” repurposing the pejorative he used for Clinton.) This may have been in part a function of Trump’s new focus on his own mental fitness.

Welcome to the race Sleepy Joe. I only hope you have the intelligence, long in doubt, to wage a successful primary campaign. It will be nasty - you will be dealing with people who truly have some very sick & demented ideas. But if you make it, I will see you at the Starting Gate! — Donald J. Trump (@realDonaldTrump) April 25, 2019

Trump’s nickname didn’t get much traction until Biden announced his candidacy in April 2019. That month, “Sleepy Joe” was mentioned more than 100 times on Fox News and — generally when quoting Trump — nearly 90 times on CNN and MSNBC combined. Over the next 19 months, Fox News would mention “Sleepy Joe” nearly 1,900 times. About 1 in 9 cable-news uses of “Sleepy Joe” since Trump developed the nickname were on Sean Hannity’s prime-time show.

That was also the point at which Biden’s age became a common topic of conversation, which wasn’t without cause. Biden was already 76, not quite two years younger than Ronald Reagan at the end of his second term. He entered a Democratic field in which he wasn’t even the oldest candidate: That title was held by Sen. Bernie Sanders (I-Vt.). As such, the Democratic nominating contest was quickly framed in generational terms.

Because the field was so crowded, the first debate took place in two parts. Biden was relegated to the second, facing off against former South Bend, Ind., mayor Pete Buttigieg and Rep. Eric Swalwell (D-Calif.), among others.

Swalwell, then 38, made repeated references to “generational” leadership. He addressed Biden on the point directly.

“I was 6 years old when a presidential candidate came to the California Democratic Convention and said, ‘It’s time to pass the torch to a new generation of Americans,’” he said. “That candidate was then-Senator Joe Biden . Joe Biden was right when he said it was time to pass the torch to a new generation of Americans 32 years ago. He’s still right today.”

In his closing comments, Buttigieg made a similar appeal: “Help me deliver that new generation to Washington before it’s too late.”

A few days later, Suffolk University released the results of a poll of Iowa voters. They determined that those who had watched the debate felt that Biden had performed the worst. Suffolk asked those who didn’t have Biden — the national front-runner — as their first or second pick why they chose another candidate. A plurality responded that Biden was too old or that they wanted someone younger.

Biden won the nomination, largely on the strength of his support among Black Americans and the perception that he was the party’s best bet for beating Trump. In early 2020, The Washington Post and our polling partners at ABC News asked Americans whether Biden and Trump had the “mental sharpness” to be president. Just over half said Biden did. Just under half said the same of Trump.

The 2020 campaign was unusual, but it wasn’t the case that Biden didn’t campaign. A Post analysis of each campaign’s events show dozens in the final weeks by both candidates. But Trump repeatedly insisted that Biden was hunkered down in his “basement” as he and his allies claimed that Biden was too mentally addled to engage in the campaign forcefully. Biden’s convention speech and debate performances served to effectively rebut those criticisms. Biden won the election.

Over the course of his presidency, The Post and ABC News have again asked Americans how they evaluate Biden’s and Trump’s mental sharpness. Views of Trump’s have improved since 2020. Views of Biden’s have declined consistently, including among members of his own party.

Polling from Pew Research Center , conducted more consistently over the course of Biden’s presidency, shows a steady decline in perceptions of Biden’s “mental sharpness.” He’s declined on other measures, too, predictably for a president whose overall approval rating has also dropped since he was first elected. But the 17-point decline on sharpness is the biggest drop by category.

There was not been substantially more coverage of Biden’s age from the beginning of his presidency until the 2022 midterms than there was from his 2019 announcement until the 2020 election. CNN and MSNBC were less likely to mention his age and mental fitness in an average month during the presidency than before it; Fox News was about equally likely to do so (though much more likely than CNN or MSNBC).

This is an imperfect proxy for media coverage of the issue, certainly. But it is a measure of it — and the decline in perceptions of Biden’s sharpness occurred with no measurable increase in cable-news chatter.

Since the midterms — and since Trump launched his 2024 candidacy — discussion of Biden’s age have increased dramatically. Both CNN and MSNBC are talking about Biden’s age and mental state more often each month on average than Fox News did before 2020. Fox News is talking about it more than twice as much as it did then.

Part of this is due to the fact that Biden is up for reelection — and that he’s four years older. Americans are quite aware of Biden’s age; polling conducted by YouGov last fall found that 6 in 10 Americans could guess Biden’s age to within two years. An 81-year-old embarking on a potential four-year commitment would raise questions in any circumstance, much less one as important as the presidency. Biden’s opponents, of course, are also happy to elevate those questions.

But they don’t only come from his opponents. An underrecognized aspect of questions about Biden’s age is that his party is heavily dependent on younger Americans. This was the pitch Swalwell and Buttigieg were making: not just that the party needed a new generation of leaders but that young Democratic voters didn’t need another older person running the country. There is a real and pervasive antipathy among younger Americans to the advanced age of political leaders, and Biden needs those younger Americans more than Trump does.

A number of things can be true … and, in this case, are. Some of the earliest attacks on Biden’s age came from Trump — and from the Democrats vying against him for the nomination. Democrats were expressing concern about Biden’s age even before the primaries began, but declining confidence in his mental sharpness came only after he was elected. The media has at times focused far more on this question than at others, but the aforementioned decline does not correlate neatly to that coverage.

Here the simplest answer is probably the correct one. Joe Biden is the oldest president in American history, and he wants to be elected to another term in office by a political party dependent on young voters. Hur’s report and the ensuing coverage aren’t helping him do that, but the problem existed even if Hur hadn’t written a thing.

An earlier version of this column incorrectly referred to Pete Buttigieg as the former mayor of Fort Wayne, Ind. He is the former mayor of South Bend, Ind.

to solve age problems

Lesson Age problems and their solutions

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Problems of Ages

Number series, miscellaneous, tricks to solve age-based problems.

Problems on ages is an important chapter for SSC/Banking and all other exams. In SSC Prelims 2 to 3 questions are asked and in mains 4 to 5 questions can be asked on this topic. As most of the questions on this topic of this chapter can be solved by analytical thinking. So, it plays a crucial role in the examination. Sometimes the question asked are confusing and complicated, so we have to learn the concept well to easily score marks for these types of questions.

Table of Contents:

1. Problems on ages :- basics and concept

2. Useful tips and tricks to solve the problems of ages

3. Important Formulas

4. Sample Questions – problems on ages

1. Problems on ages – basics and concept          Problems on ages basically consist of information about the ages of two or more persons and a relationship between their ages in the past/present/future.

In the quantitative aptitude section( banking /SSC exams) the problems on ages are kind of brain teasers,  at the very first time when a candidate studies this it may seem to be complex, but it becomes easy when solved step by step. 

In the quantitative aptitude sector problems on ages mostly are asked for 2-3 marks but there may be a possibility of age-based questions being asked as a part of the data sufficiency or data interpretation. So it is very important to clarify the concept to each and every candidate. 

The useful tips given below are for the Candidates who are not much familiar with the concept and tendency to skip the problems on ages or answer them incorrectly. These tips may help you to clear the concept and answers the questions correctly.

I) To read the question carefully and gradually form the equation is the most important thing. It helps you answer the question.

II) Basic things like subtraction, addition, multiplication, and division will help a candidate reach the answer and no complicated calculations are required to answer these questions.

III) Arrange the values correctly and use them as linear equations.

IV) Once the linear equation has been formed, solve the equation to find the answer.

V) The final step is to recheck the answer obtained by placing it in the equation formed to ensure that no error has been made while calculating.

The ‘problems on ages’ is one such topic which is not just asked in the preliminary phase of the examination but questions from this topic may also be asked in the main examination in a rather complex manner.

The formulas given below are related to the problems on ages which may help you to answer the problems quicker and also get a better idea of the concept:-

I) Suppose if the present age of a person is x, then after n years, the age of the person will be (x+n) years.

II) Suppose if the present age of a person is x, then before n years the age of the person will be (x-n) years.

III) Suppose the ratio of two persons is p : q, then their age will be px and qx respectively.

IV) Suppose the present age of a person is x, then  n times the present age will be (x * n) years

V) Suppose the present age of a person is x, then 1/n of the age shall be equal to (x/n) years

These formulas and tricks will help you in solving the questions easily and more efficiently.  

1. Question Five years ago the ratio of the ages of Amit and Neha was 8 : 7. Three years hence, the ratio of their ages will be 12 : 11. what is Neha’s age at present?

A) 13 years

B) 16 years

D) 19 years

E) None of these

Answer:- D Explanation:-

Let the age of Amit and Neha five years ago 8x and 7x respectively.

Amit’s present age = (8x + 5)

Neha’s present age = (7x + 5)

Now, as per the equation,

{(8x + 5) + 3} /{( 7x + 5) + 3} = 12/11                          => (8x + 8)/(7x + 8) = 12/11

=>  88x + 88 = 84x + 96  

=>  4x = 8  

⇒  x = 2.  

 ∴     Neha’s present age = (7x + 5) = (7 × 2 + 5) = 19 years.

Hence, option D is correct.

Amit : Neha =  8 : 7      ( -5)

                     = 12 : 11   (+3)

= ( – 5 + 3 ) = 2

So, Neha’s age = 7 × 2 = 14

Neha’s present age = 14 + 5 = 19 years  

Or, Neha’s age = 11 × 2 = 22

Neha’s present age = 22 – 3 = 19 years

2.Question The present ages of the three friends are in the ratio 3 : 5 : 7. Eight years ago, the sum of their ages was 96. find the sum of the present ages of the first two friends (in years)?

A) 42 years

B) 64 years

C) 70 years

D) 67 years

Answer:- B Explanation:-

Let the present age of three friend’s are = 3x, 5x and 7x

(3x – 8) + (5x – 8) + (7x – 8) = 96

15x – 24 = 96  15x = 120 x = 8

Their present ages are 24 years, 40 years and 56 years respectively. The sum of the present ages of the first two friends = ( 24 + 40) = 64 years Hence, option B is correct.

3. Question The ratio of the father’s age to his son-in-law’s age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :

Answer – D  Explanation:-

Let the present ages of Father and son-in-law be 9x and 5x respectively.

9x × 5x = 1125       45×2 = 1125        x2 = 25    x = 5.

Required ratio  = (9x + 5) : (5x + 5)  ⇒   50 : 30  ⇒  5 : 3.  

4. Question The total ages of Aman, Nageshwar and Satyam is 96 years. The ratio of their ages before 5 years was 2 : 3 : 4. What is the present age of Aman?

A) 23 years

B) 32 years

C) 21 years

D) 33 years

Answer:- A Explanation:-

Let the ages of Aman, Nageshwar and Satyam 5 years ago be 2x, 3x and 4x years respectively.

So, total of their present ages will be,

(2x + 5) + (3x +5) + (4x + 5) = 96 => 9x + 15 = 96 => 9x = 81 x = 9.

So, the present age of Aman =( 2x + 5 )=( 2 × 9 + 5 )= 23 years.

Hence, option A is correct.

5. Question The ratio of the present ages of two boys is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?.

Answer :-. B Explanation:-

Assume 2x and 3x be the present age of two friends respectively. 

Then,      2x – 6  = 1 3x – 63 ⇒ 6x – 18 = 3x – 6   ⇒  3x  = 12   ⇒  x = 4.

So,  required ratio = (2x + 4) : (3x + 4)  ⇒  12 : 16  ⇒  3 : 4.  

Hence, option B is correct.

2 : 3    —– ( × 2)  = 4 : 6   (× 2)  = 8 : 12

1 : 3    —– ( × 1)  = 1 : 3  ( × 2)  = 2 : 6

So, the present ages of the two boys 8 years and 12 years respectively.

4 years later their ages will be (8+4) = 12 years and (12+4)= 16 years.

Ratio = 12 : 16 = 3 : 4.

6. Question mother’s age is twice of her daughter. Before ten years, she was twelve times as old as her daughter. What is the sum of the present age of a mother and her daughter together?

A) 33 years

B) 36 years

C) 40 years

D) 26 years

Answer:-.  A Explanation:-

Let, the present age of daughter = p 

Present age of her mother = 2p

10 yr back, the ratio of their ages was = 12: 1

(2p – 10)/(p – 10) = 12 /1 => 2p – 10 = 12p – 120 => 10p = 110 => P = 110/10 = 11

Present age of daughter = 11 years

Present age of mother = 11× 2 = 22 years

Thus, the sum of the present age of mother and her daughter 

= 22+11 yrs = 33 years Here , A is the correct answer. 

Mother : Daughter =  2 : 1     (× 11)  = 22 : 11

                                 = 12 : 1   ( × 1)   = 12 : 1

Present age of Mother = 22 years

Present age of Daughter = 11 years

Thus, Sum of their ages = 22 + 11  = 33 years.

7. Question Amit is 2 years older than Bikash who is twice as old as Chetan. If the sum of the present ages of Amit, Bikash and Chetan be 52, then how old is Bikash?

A) 20 years B) 22 ears C) 15 years D) 13 years E) 21 years

Answer: A Explanation :-

Let the present age of Chetan = x years

So, Bikash’s present age = 2x

And Amit’s present age = 2x + 2

According to the question,

x+2x+2+2x = 52

So, Bikash’s age = 2×10 = 20 years Here ,the correct option is A .

8. Question In a family, of five-person, the total age of the elder brother and younger brother is 56 years and after four years the age of the elder brother will be three times that of the younger brother. What is the age of the two brothers respectively?

A) 12 years, 41 years              B) 15 years, 53 years C) 11 years, 34 years D) 12 years, 44 years E) 21 years, 42 years

Let the present age of the elder brother = x years The present age of the younger brother = y years

According to the question,  x+y = 56     ————-(1)

After 4 years, age of the elder brother = x+4

after 4 years the age of younger brother = y+4

x+4 = 3 (y+4)     ———–(2)

x+4 = 3y + 12

From the equation (1) we get,  x = 56-y

Now putting the value of x in equation 2, we get

(56-y) + 4 = 3y + 12

⇒60 – y = 3y + 12

So, the younger brother’s present age is =12 years

the elder brother’s present age = 56-12 = 44 years

Here the correct answer is D.

9. Question Akash is as much elder than Vijay as he is younger to Ketan and the sum of the ages of Vijay and Ketan is 48 yr, then find the age of Akash.

A) 36 years B) 24 years C) 27 years D) 18 years E) 22 years

Answer:- B Explanation:- Let the present age of Akash = x years and he is younger to Ketan by y years  Then, Ketan’s age = (x + y) years Vijay’s age = (x – y) years

Now, according to the question, Sum of ages of Ketan and Vijay = 48 (x + y) + (x – y) = 48 2x = 48 years x = 24 years

Hence, present age of Akash is 24 yr.

10. Question Your uncle is three times as old as you. 15 yr hence, your uncle will be twice as old as you. What is the sum of the present ages of you and your uncle?

A) 60 years B) 55 years C) 75 years D) 50 years E) none of these

Answer :- A Explanation :- Let, the present ages of your uncle and you be 3x and x years respectively

15 years later, ratio between your uncle and your age = 2 :1

Now, (3x + 15)/(x + 15) = 2/1 => 3x + 15 = 2x + 30 => x = 15

Thus, Sum of the ages of your uncle and your  = ( 3x + x ) = 4 × 15 = 60 years Here the correct answer is A .

11. Question The present age of Kamal is 5 times the age of Shiva. After 10 yr, Kamal will be 3 times as old as Shiva. What are the present ages of Kamal and Shiva?

A) 45 years, 9 years B) 55 years, 11 years C) 65 years, 13 years D) 40 years, 8 years E) 50 years, 10 years

Answer :- E Explanation:- Let the present age of Shivam = x years

Then, present age of Kamal = 5x years

After 10 years, the ratio of ages of Kamal and Shiva = 3 : 1

(5x + 10)/(x + 10) = 3/1 => 5x + 10 = 3x + 30 => 2x = 20 => x = 10

Present age of Shiva = 10 years Present age of Kamal = 10×5 = 50 years

12. Question 5 yr ago, the age of Sanjay was 4 times the age of Vikram and after 10 yr, Sanjay will be twice as old as Vikram. Find the present ages of Sanjay and Vikram.

A) 35 years, 12.5 years

B) 33 years, 11 years

C) 45 years, 16 years

D) 50 years, 18.5 years

Explanation:-

Let the present ages of Sanjay and Vikram be x years and y years, respectively.

According to the question, 5 years ago,

(x – 5)/( y – 5) = 4/1 => x – 5 = 4y  – 20 => x = 4y – 15      —————–(1)

10 years later, ( x + 10)/(y + 10) = 2 : 1 => x + 10 = 2y + 20 => x = 2y + 10      —————-(2)

Equating both the equations (1) and (2) ,we get,

4y – 15 = 2y + 10 => 2y = 25 => y = 12.5

Putting the value of y in equation (2),we get,

x = 2 × 12.5 + 10 => x = 35

Thus,the present age of Sanjay = 35 years And the present age of Vikram = 12.5 years

13.Question Four years ago, Sharma’s age was 3/4 times that of Raman. Four years hence, Sharma’s age will be 5/6 times that of Raman. What is the present age of Sharma?

(a) 16 yrs (b) 20 yr  (c) 15 yr  (d) 24 yr (e) 8 yr

Answer :-A Explanation :-

4 years ago,  let, Raman’s age = x years And Sharma’s age = 3x/4 years

Now, Present age of Raman = x + 4 years And present age of Sharma =( 3x/4 + 4 ) years

5/6 ( x + 4 + 4) = (3x/4 + 4 + 4) => 5/6 ( x + 8) = ( 3x/4 + 8) => 4(5x + 40) = 6( 3x + 32) => 20x + 160 = 18x + 192 => 2x = 32 => x = 16

Thus the present age of Sharma  =( 3/4 × 16 + 4) years = 16 years Here the correct answer is A.

14. Question The present ages of the two women are 36 and 50 yr, respectively. After p years, the ratio of their ages will be 3 : 4, then find the value of p.

(e) none of these

Answer :-C Explanation :-

According to the question, (36 + p)/( 50 + p) = 3/4 => 144 + 4p = 150 + 3p => p = 6 Thus, the value of p = 6.

15. Question The present ages of Rohit and Urvashi are 36 and 48 yr, respectively. What was the ratio between the ages of Urvashi and Rohit respectively 8 yr ago?

(e) None of the above

Answer :- D Explanation :-

Ratio = (48 – 8) : (36 – 8)          = 40 : 28          = 10 : 7 Here the correct answer is D.

16. Question The average age of two teachers is 35 yr. The average age of the two teachers and a student is 27 yr. What is the age of the student?

(c) 10.5 yr

Answer :- A

Explanation :-

Total age of two teachers = 35 x 2 = 70 yr

and total age of two teachers and students together

= 27 x 3 = 81 yr

: Age of the student = 81-70 = 11 yr

17.Question The average of the present ages of Saikat and Shivani is 36 yr. If Saikat is 8 yr older than Shivani, what is the Shivani’s present age?

Answer :- C

Total age of Saikat and Shivani

= 36 × 2 = 72 yr

Let age of Shivani = x yr

Then, age of Saikat = (x + 8) yr

Hence, Shivani’s present age = 32 years  

18. Question

The ratio between the present ages of Irfaan and Kapil is 3 : 8. After 8 years, Irfaan’s age will be 20 yr. What was Kapil’s age 5 years hence?

Answer :-A Explanation:- Let present ages of Irfaan and Kapil are

3x years and 8x years respectively.

3x + 8 = 20

=> 3x = 12

Kapil’s present age = 8x = 8×4 = 32 years

Hence, Kapil’s age 5 years hence = 32+5 = 37 years

19. Question The ratio between the present ages of Tanmay and Vivek is 3:7, respectively. After 4 yr, Vivek’s age will be 39 yr. What was Tanmay’s age 4 yr later?

Answer :- C Explanation :-

Let Tanmay and Vivek’s ages are 3x yr and 7x yr, respectively. 7x + 4 = 39 ⇒ x = 5 =3×5-4=11 yr Hence, Tanmay’s age 4 yr later = 3×5 + 4  = 19 years.

20. Question

The average age of a group of five girls is 24. If the present age of the youngest girl is 8 year, what was the average age of the group at the time of the birth of the youngest girl?

Total age of the group of five girls

= 24 x 5 = 120

Total age of four girls at the time of

birth of youngest girl=( 120 – 8×5) years

= 120 – 40 = 80 years

Hence, required average age = 80/4 = 20 yr

Hence the correct answer is E.

21. Question 30. The present age of Rahul’s mother is four times Rahul’s present age. Five years ago, Rahul’s mother was seven times as old as Rahul. What is the present age of Rahul’s mother?

Let the present age of Rahul = x.

Then, present age of Rahul’s mother= 4x

Now, 5 yr ago,

Rahul’s mother’s age = 7 x Rahul’s age

4x -5= 7(x – 5)

=> 4x – 5 = 7x – 35

=>3x = 30

=>x = 10

.. Rahul’s present age = x= 10 years

.. Rahul’s mother’s present age= 4x  = 4 x 10 = 40 yr

22. Question The age of Prakash is three times Arvind’s age. After 7 yr, Prakash will be twice Arvind’s age, then how many times will Prakash’s age be in another 14 yr time with respect to Arvind’s age then?

Let Arvind’s age = x yr

Then, Prakash’s age = 3x yr

3x + 7 = 2(x + 7)

3x + 7 = 2x + 14

:: Age of Arvind after 14 yr = 7+ 14 = 21 yr

Prakash’s present age = 21 yr

Hence, Prakash’s age is one time of Arvind’s age.

23. Question

10 years ago, the ratio of ages of a man and a woman was 13:17. After 17 years from now, the ratio of their ages will be 10:11 . What is the present age of the woman?

Let the ages of man and woman 10 yr before were 13x yr and 17x yr, respectively.

Then, present age of man = 13x + 10

and present age of woman = 17x + 10

 (13x + 10 + 17)/(17x + 10 + 17) = 10/11

=> (13x + 27)/(17x + 27) = 10/11

=> 143x + 297 = 170x + 270

=> 27x = 27

=> x = 1

Hence ,the present age of the woman  = (17×1 + 10) = 27 years

24.Question Kailash age is twice of Shekher’s age. 8 yr hence, the respective ratio between Kailash’s and Shekhar’s ages will be 22:13.What is Kailash’s present age?

(b) 18 yr (d) 30 yr (a) 26 yr (c) 42 yr (e) None of the above

Answer:- E Explanation:- Let Shekhar’s present age = x yr Then, Kailash’s present age = 2x yr According to the question, (2x + 8)/(x + 8 ) = 22/13 26x + 104 = 22x + 176 4x = 72 x = 18 Hence, Kailash’s age = 2 x 18 = 36 yr

25.Question Before 7 years, the ages of P and Q were in the ratio 4:5 and 7 yr hence, they will be in the ratio 5: 6. Find the age of Q in present.

Let, 7 yr ago, ages of P and Q were 4x years and 5x years, respectively.

Then, present age of P = 4x + 7  and present age of Q = 5x + 7

Now, according to the question,

(4x + 7+ 7)/(5x +7+7) =5/6

24x + 84 = 25x + 70

Hence, Q’s present age =(5x + 7)

= 5×14 + 7 years

= 77 years.

Hence the correct answer is D.

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Course: Algebra 1   >   Unit 6

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Age word problems

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  • Your answer should be
  • an integer, like 6 ‍  
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  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • Equation Problems of Age

Equation Problems of Age are part of the quantitative aptitude section. In the equation problems of age, the questions are such that they result in equations. These equations could become either linear or non-linear and they will have solutions that will represent the age of the people in the question. In the following sections, we will some of the examples of these problems and also learn about the various shortcuts that we can use to solve them. Let us start with some easier examples and concepts below.

Suggested Videos

Equations are a convenient way to represent conditions or relations between two or more quantities . An equation could have one, two or more unknowns. The basic rule is that if the number of unknowns is equal to the number of conditions, then these equations are solvable, otherwise not. We will see some important examples here but first, let us see the following tricks.

If the age of a person is ‘x’, then ‘n’ years after today, the age = x + n. Similarly, n years in the past, the age of this would have been x – n years.

Example 1: A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be:

A) 23 years               B) 19 years                  C) 20 years                        D) 22 years

Answer: Suppose that the present age of the son is = x years. Then the father’s age is (60 -x) years. Notice that we are trying to reduce the problem into as few variables as possible. As per the second condition of the question, we have:

The age of the father six years ago = (60 – x) – 6 years = 54 – x years.

Similarly the age of the son six years ago will be x – 6 years. Therefore as per the second condition , we have;

54 – x = 5(x – 6) or 54 – x = 5x – 30 and we can write 6x = 84

Hence, we have x = 14 years. Thus the son’s age after 6 years = (x+ 6) = (14 + 6) = 20 years. Hence the correct option is C) 20 years.

More Solved Examples

Example 2: The difference in the age of two people is 20 years. If 5 years ago, the elder one of the two was 5 times as old as the younger one, then their present ages are equal to:

A) 20 and 30 years respectively

B) 30 and 10 years respectively

C) 15 and 35 years respectively

D) 32 and 22 years respectively

Answer: The first step is to find the equation. Let the age of the younger person be x. Then the age of the second person will be (x + 20) years. Five years ago their ages would have been x – 5 years and x + 20 years. Therefore as per the question, we have: 5 (x – 5) = (x + 20 – 5) or 4x = 40 or x = 10. Therefore the ages are 10 years for the younger one and (10 + 20) years = 30 years for the elder one.

Example 3: Yasir is fifteen years elder than Mujtaba. Five years ago, Yasir was three times as old as Mujtaba. Then Yasir’s present age will be:

A) 29 years                  B) 30 years                     C) 31 years                        D) 32 years

Answer: Let the age of Yasir be = x years. Then the age of Mujtaba will be equal to x – 15 years. Now let us move on to the second condition. Five years ago the age of Yasir will be equal to x – 5 years. Also, the age of Mujtaba five years ago will be x – 15 – 6 years = x – 21 years. As per the question, we have:

3(x – 21) = x – 5 or 3x – 63 = x  – 5. Therefore we have: 2x = 58 and hence x = 29 years. Therefore Yasir’s present age is 29 years and the correct option is A) 29 years.

Example 4: Ten years ago, the age of a person’s mother was three times the age of her son. Ten years hence, the mother’s age will be two times the age of her son. The ratio of their present ages will be:

A) 10:19                        B) 9: 5                                 C) 7: 4                                      D) 7: 3

Answer: Let the age of the son ten years ago be equal to x years. Therefore the age of the mother ten years ago will be equal to 3x. Following this logic, we see that the present age of the son will be equal to x + 10 years and that of the mother will be equal to 3x + 10 years.

The second condition says that ten years from the present, the mother’s age will be twice that of her son. After ten year’s the mother’s age will be 3x + 10 + 10 years and that of the son will be x + 10 + 10 years. As per the question we have:

(3x + 10) +10 = 2 [(x + 10) + 10] or (3x + 20) = 2[x + 20]. In other words , we can write:

x = 20 years. Thus the present age of the mother = 3(20) + 10 = 70 years. Also the present age of the son = 20 + 10 = 30 years. Thus the ratio is 7:3 and the correct option is D) 7:3.

Practice Questions

Q 1: The age of a man is 24 years more than his son. In two years, the father’s age will be twice that of his son. Then the present age of his son is: A) 18 years                   B) 21 years               C) 22 years                 D) 24 years

Ans: C) 22 years.

Q 2: After 15 years Ramesh’s age will be 5 times his age 5 years ago. What is the present age of Ramesh? A) 5 years                     B) 10 years               C) 15 years                  D) 20 years

Ans: B) 10 years

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6 responses to “Ratio Based Age Problems”

3 peoples ages = 100,the older is 5 years older than the second,the age of the third is half of the seconds age ,whats the age of the thrid person ?

The ages of zaira and angel are in the ratio 7:9. Five years ago, the sum of their ages is 54. What are their present ages?

Am I crazy or is Q1 not the right answer? I got 24. I even looked this up elsewhere and people were reporting 24 is the correct answer (or rather none of the above in this case).

5 Read the information given. Form simultaneous equations and solve :

Present age of Raju is X years

Present age of Sanju is y years

Add 4 years , to their ages

The ratio of their ages is

Equation 121

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Biden has a huge decision to make — one of the most important of his presidency

  • President Biden is a lifelong public servant, and he's behind in polls for reasons he can't change.
  • So, for the sake of the country, Biden has a critical decision to make:
  • Whether or not to step aside so the Democrats can nominate another candidate.

Insider Today

President Joe Biden has dedicated almost his entire professional life to serving our country.

This summer, he will have another critical opportunity to do that.

Specifically, he will have to make a decision that, in my opinion, could determine the future of American democracy.

That decision is this:

Whether to accept his party's nomination to run for a second term… or step aside and let the Democrats nominate another candidate.

Whether or not you believe that "democracy is on the ballot" this fall (or care), you will probably agree that the stakes in this election are unusually high. So, at their convention this summer, the Democrats will want to nominate the  strongest possible candidate .

Based on recent polls, it does not seem that Biden is necessarily the  strongest possible candidate .

And even once he finishes sweeping the primaries, Biden does not necessarily  have to be the candidate.

Because, as political experts explain , Biden could still step aside before the Democratic convention this August and allow the Democrats to nominate someone else.

So, over the next six months, for the sake of his country — or at the very least the Democratic party and its policy objectives — Biden needs to dispassionately assess whether he is, in fact, the strongest possible candidate . If not, he should step aside.

In making this decision, Biden needs to look and think carefully about not what is "true" or "right" or about what he wants most Americans to think, but what Americans actually think.

According to recent polls, even in our polarized country, most Americans actually agree about several things.

One is that ex-President Trump would do a better job than Biden  on the economy (mostly, it seems, because of still-high inflation). Another is that Trump would do  better on immigration , another highly visible issue. A third is that most Americans ( a remarkable 81% of us ) think that Biden is too old to run for president. (Most of us think Trump is too old, too, but fewer of us.)

In a diverse country, 81% is a startling and resounding consensus.

What’s more,  76% of us have either "major" or "moderate" concerns  about Biden’s mental and physical fitness for a second term.

Now, maybe all of that is just unfairness or perception. Maybe Americans who think those things are just being stupid or falling for oppositional propaganda or are just being worrywarts.

But here’s the thing:

When it comes to elections,  perception is reality .

And, for most voters, our current  perception  is that Trump is the less bad and less old of two weak candidates that most Americans have deep misgivings about.

If, despite Biden’s age, Americans agreed he was doing a bang-up job as president or were thumping Trump in the polls, we could dismiss these concerns.

But only  37% of us approve  of the job Biden is doing.

And Biden is now  trailing ex-Pres. Trump in the swing-state polls and losing to him in the betting markets .

True — the election is nine months away.

True — a lot might change before then, including the polls.

But the way things stand today, it looks to many like Biden’s decision to accept the Democratic nomination might affect the future of America’s democracy — and, with it, the Constitution and country that Biden has sworn to protect.

Of course, a key factor in deciding whether to step aside is whether there is  anyone else  the Democrats could nominate who could be a  stronger  candidate.

Polls suggest, for example, that it would be stupid for Biden to step aside so the Democrats can nominate Vice President Kamala Harris because she  would do even worse  against Trump.

But most potential Democratic candidates deferred to Biden's desire to enter the primaries and didn't enter the race, so I don't think we really know yet whether there is a stronger candidate. By nominating someone at the convention, moreover, Democrats can choose the candidate they think has the best chance to win the general election , as opposed to the one that appeals most to Democratic voters in the primaries.

As New York Times columnist Ross Douthat  has explained , it would be better if Biden waited until mid-summer to make (or at least announce) his decision:

The next six months would provide time to see whether the polls change meaningfully — a key factor in the analysis. The waiting period would also give the broader Democratic party time to figure out whether anyone else might make a stronger candidate. And it would allow more of Trump's legal trials to play out.

If, by early August, the analysis suggests that Biden is, in fact, the strongest candidate, then the best way to serve his country would be to accept the nomination. If, on the other hand, Biden concludes that someone else might have a better chance, he could serve his country better by dropping out.

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Watch: Joe Biden is running for reelection, and Trump slammed the announcement

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I’m a Neuroscientist. We’re Thinking About Biden’s Memory and Age in the Wrong Way.

President Biden seated in a chair holding a stack of what looks like index cards.

By Charan Ranganath

Dr. Ranganath is a professor of psychology and neuroscience and the director of the Dynamic Memory Lab at the University of California, Davis, and the author of the forthcoming book “Why We Remember: Unlocking Memory’s Power to Hold On to What Matters.”

The special counsel Robert K. Hur’s report, in which he declined to prosecute President Biden for his handling of classified documents, also included a much-debated assessment of Mr. Biden’s cognitive abilities.

“Mr. Biden would likely present himself to a jury, as he did during our interview with him, as a sympathetic, well-meaning, elderly man with a poor memory.”

As an expert on memory, I can assure you that everyone forgets. In fact, most of the details of our lives — the people we meet, the things we do and the places we go — will inevitably be reduced to memories that capture only a small fraction of those experiences.

It is normal to be more forgetful as you get older. Generally, memory functions begin to decline in our 30s and continue to fade into old age. However, age in and of itself doesn’t indicate the presence of memory deficits that would affect an individual’s ability to perform in a demanding leadership role. And an apparent memory lapse may or may not be consequential, depending on the reasons it occurred.

There is forgetting, and there is Forgetting. If you’re over the age of 40, you’ve most likely experienced the frustration of trying to grasp that slippery word on the tip of your tongue. Colloquially, this might be described as forgetting, but most memory scientists would call this retrieval failure, meaning that the memory is there but we just can’t pull it up when we need it. On the other hand, Forgetting (with a capital F) is when a memory is seemingly lost or gone altogether. Inattentively conflating the names of the leaders of two countries would fall in the first category, whereas being unable to remember that you had ever met the president of Egypt would fall into the second.

Over the course of typical aging, we see changes in the functioning of the prefrontal cortex, a brain area that plays a starring role in many of our day-to-day memory successes and failures. These changes mean that as we get older, we tend to be more distractible and often struggle to pull up words or names we’re looking for. Remembering events takes longer, and it requires more effort, and we can’t catch errors as quickly as we used to. This translates to a lot more forgetting and a little more Forgetting.

Many of the special counsel’s observations about Mr. Biden’s memory seem to fall in the category of forgetting, meaning that they are more indicative of a problem with finding the right information from memory than Forgetting. Calling up the date that an event occurred, like the last year of Mr. Biden’s vice presidency or the year of his son’s death, is a complex measure of memory. Remembering that an event took place is different from being able to put a date on when it happened, which is more challenging with increased age. The president very likely has many memories, even though he could not immediately pull up dates in the stressful (and more immediately pressing) context of the Oct. 7 attack on Israel.

Other “memory” issues highlighted in the media are not so much cases of forgetting as they are of difficulties in the articulation of facts and knowledge. For instance, in July 2023, Mr. Biden mistakenly stated in a speech that “we have over 100 people dead,” when he should have said, “over one million.” He has struggled with a stutter since childhood, and research suggests that managing a stutter demands prefrontal resources that would normally enable people to find the right word or at least quickly correct errors after the fact.

Americans are understandably concerned about the advanced age of the two top contenders in the coming presidential election (Mr. Biden is 81, and Donald Trump is 77), although some of these concerns are rooted in cultural stereotypes and fears around aging. The fact is that there is a huge degree of variability in cognitive aging. Age is, on average, associated with decreased memory, but studies that follow up the same person over several years have shown that although some older adults show precipitous declines over time, other super-agers remain as sharp as ever.

Mr. Biden is the same age as Harrison Ford, Paul McCartney and Martin Scorsese. He’s also a bit younger than Jane Fonda (86) and a lot younger than the Berkshire Hathaway C.E.O., Warren Buffett (93). All these individuals are considered to be at the top of their professions, and yet I would not be surprised if they are more forgetful and absent-minded than when they were younger. In other words, an individual’s age does not say anything definitive about the person’s cognitive status or where it will head in the near future.

I can’t speak to the cognitive status of any of the presidential candidates, but I can say that, rather than focus on candidates’ ages per se, we should consider whether they have the capabilities to do the job. Public perception of a person’s cognitive state is often determined by superficial factors, such as physical presence, confidence and verbal fluency, but these aren’t necessarily relevant to one’s capacity to make consequential decisions about the fate of this country. Memory is surely relevant, but other characteristics, such as knowledge of the relevant facts and emotion regulation — both of which are relatively preserved and might even improve with age — are likely to be of equal or greater importance.

Ultimately, we are due for a national conversation about what we should expect in terms of the cognitive and emotional health of our leaders.

And that should be informed by science, not politics.

Charan Ranganath is a professor of psychology and neuroscience and the director of the Dynamic Memory Lab at the University of California, Davis, and the author of “ Why We Remember: Unlocking Memory’s Power to Hold On to What Matters .”

The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips . And here’s our email: [email protected] .

Follow the New York Times Opinion section on Facebook , Instagram , TikTok , X and Threads .

Algebra Age-Related Word Problem Worksheets

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Problem-Solving to Determine Missing Variables

Many of the  SAT s, tests, quizzes, and textbooks that students come across throughout their high school mathematics education will have algebra word problems that involve the ages of multiple people where one or more of the participants' ages are missing.

When you think about it, it is a rare opportunity in life where you would be asked such a question. However, one of the reasons these types of questions are given to students is to ensure they can apply their knowledge in a problem-solving process.

There are a variety of strategies students can use to solve word problems like this, including using visual tools like charts and tables to contain the information and by remembering common algebraic formulas for solving missing variable equations.

Birthday Algebra Age Problem

 Deb Russell

In the following word problem, students are asked to identify the ages of both of the people in question by giving them clues to solve the puzzle. Students should pay close attention to key words like double, half, sum, and twice, and apply the pieces to an algebraic equation in order to solve for the unknown variables of the two characters' ages.

Check out the problem presented to the left: Jan is twice as old as Jake and the sum of their ages is five times Jake's age minus 48. Students should be able to break this down into a simple algebraic equation based on the order of the steps, representing Jake's age as a and Jan's age as 2a : a + 2a = 5a - 48.

By parsing out information from the word problem, students are able to then simplify the equation in order to arrive at a solution. Read on to the next section to discover the steps to solving this "age-old" word problem.

Steps to Solving the Algebraic Age Word Problem

First, students should combine like terms from the above equation, such as a + 2a (which equals 3a), to simplify the equation to read 3a = 5a - 48. Once they've simplified the equation on either side of the equals sign as much as possible, it's time to use the distributive property of formulas to get the variable  a  on one side of the equation.

In order to do this, students would subtract 5a  from both sides resulting in -2a = - 48. If you then divide each side by -2 to separate the variable from all real number in the equation, the resulting answer is 24.

This means that Jake is 24 and Jan is 48, which adds up since Jan is twice Jake's age, and the sum of their ages (72) is equal five times Jake's age (24 X 5 = 120) minus 48 (72).

An Alternate Method for the Age Word Problem

No matter what word problem you're presented with in algebra , there's likely going to be more than one way and equation that's right to figure out the correct solution. Always remember that the variable needs to be isolated but it can be on either side of the equation, and as a result, you can also write your equation differently and consequently isolate the variable on a different side.

In the example on the left, instead of needing to divide a negative number by a negative number like in the solution above, the student is able to simplify the equation down to 2a = 48, and if he or she remembers, 2a is the age of Jan! Additionally, the student is able to determine Jake's age by simply dividing each side of the equation by 2 to isolate the variable a.

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Age Word Problems

Grade 8 math worksheets.

Age word problems involve finding the age of one or more individuals at a given point in time, based on the information provided in the problem.

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Here are some examples of age word problems:

There are no specific formulas for age word problems. However, there are some general steps that can be followed to solve age word problems:

Steps to solve age word problems

Step 1: Read the problem carefully and identify the unknowns. Usually, the problem will ask for the age of one or more individuals at a specific point in time.

Step 2: Assign variables to represent the unknowns. Let’s say, for example, that the problem asks for the age of person A at a specific point in time. Then we can assign the variable A to represent that age.

Step 3: Use the information provided in the problem to set up one or more equations that relate the unknowns to each other.

Step 4: Solve the equations to find the values of the unknowns.

Step 5: Check your answer by making sure it satisfies all the conditions given in the problem.

It is important to note that age word problems can vary in complexity and may require additional steps or mathematical concepts to solve.

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Example 1 :

Lisa is 20 years older than Tom. In 5 years, Lisa’s age will be twice Tom’s age. How old is Tom now? Solution: Let’s assume Tom’s current age is x. Then Lisa’s current age is x+20. In 5 years, Tom’s age will be x+5 and Lisa’s age will be x+25. According to the problem, Lisa’s age in 5 years will be twice Tom’s age in 5 years. So we can write an equation: x+25 = 2(x+5). Solving this equation, we get x=15. Therefore, Tom is currently 15 years old.

John is twice as old as Mary was when John was as old as Mary is now. If Mary is 20 years old, how old is John? Solution:Let’s say: Mary’s current age = M John’s current age = J

According to the information given, John is twice as old as Mary was when John was as old as Mary is now. This means that the age difference between John and Mary remains constant.

Let’s say x represents the number of years ago when John was as old as Mary is now. At that time, John’s age was (J – x), and Mary’s age was (M – x).

We are given that Mary is currently 20 years old, so M = 20.

From the information above, we can create the following equation: J = 2(M – x)

Now let’s substitute M with 20 in the equation: J = 2(20 – x)

Since John’s current age is J and Mary’s current age is M, we know that J = M. Substituting J with M in the equation, we have: M = 2(20 – x)

Since we know that M = 20, we can solve for x: 20 = 2(20 – x) 20 = 40 – 2x 2x = 40 – 20 2x = 20 x = 10

Now that we have x = 10, we can find John’s current age by substituting x back into the equation J = 2(20 – x): J = 2(20 – 10) J = 2(10) J = 20

Therefore, John is currently 20 years old.

Alex is 5 years older than Bob, and Carol is twice as old as Alex. The sum of their ages is 66. How old is Bob? Solution: Let’s assume Bob’s current age is x. Then Alex’s current age is x+5, and Carol’s present age is 2(x+5)=2x+10. According to the problem, the sum of their ages is 66. So we can write an equation: x+(x+5)+(2x+10)=66. Solving this equation, we get x=12.75. Therefore, Bob is currently 12.75 years old.

Jane is 10 years younger than John. In 5 years, Jane’s age will be half of John’s age. How old is John now? Solution: Let’s assume John’s current age is x. Then Jane’s current age is x-10. In 5 years, John’s age will be (x+5) Jane’s age will be (x-10)+5 Jane’s age will be x+5 According to the problem, Jane’s age will be age on 5 years will half John’s age, x-5 = 1/2 (x+5) 2(x-5) = (x+5) 2x-10 = x+5 2x -x = 10 + 5 x = 15 John’s age will be 25 years.

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Age Word Problems FAQS

What are age word problems, what are some tips for solving age word problems.

Some tips for solving age word problems include carefully reading the problem, identifying the unknowns, assigning variables to represent the unknowns, using the information provided in the problem to set up equations, solving the equations, and checking your answer.

What mathematical concepts are commonly used in age word problems?

Age word problems may involve algebraic equations, linear equations, systems of equations, and other mathematical concepts.

How do I know which equation to use for an age word problem?

The equation you use for an age word problem depends on the specific information given in the problem. It is important to carefully read and analyze the problem to determine which equation or equations will be necessary to solve it.

How do I check my answer for an age word problem?

You can check your answer for an age word problem by making sure it satisfies all the conditions given in the problem. For example, if the problem states that the sum of the ages of three people is 50, you can check your answer by adding up the ages you found for each person and making sure the total is 50.

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Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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A psychologist explains how couples can defeat the ‘motherhood penalty’.

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As women juggle their career and family responsibilities, they often find themselves stretched thin. ... [+]

Women make up nearly half of the workforce in the United States and a significant portion of these women are mothers. According to a 2023 report , approximately 71% of mothers with children at home are employed. Additionally, the Center for American Progress notes that in 41% of American households with children, women serve as the primary or sole breadwinner. Despite these statistics, becoming a mother often results in decreased earnings and earning potential for women.

Research shows that the earnings gap between heterosexual spouses doubles between two years before the birth of their first child and one year after. This gap widens until the child reaches age 10 and, although it may decrease thereafter, it never fully disappears—a phenomenon known as the “Motherhood Penalty.”

To explain this, a 2020 study identified several factors contributing to the widening motherhood wage gap, estimated at approximately 3.6-3.8%.

  • Wage disparities concerning the total number of children result from mothers’ reduced work experience and missed career prospects due to childcare duties.
  • Conversely, disparities linked to having one child predominantly arise from mothers choosing lower-paying positions, often to accommodate child care duties or due to biases in the labor market, thereby exacerbating the wage gap compared to child-free women.

The implications extend beyond the workplace, affecting a woman’s personal life in the following ways:

  • Reduced income can strain household finances and lead to family tension
  • Feeling undervalued professionally can impact a woman’s self-esteem and overall happiness
  • The motherhood penalty influences family dynamics, potentially leading to relationship strains and heightened stress at home
  • Balancing career and family obligations often results in women sacrificing their well-being, feeling overwhelmed and emotionally drained

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Here are three ways you can help your partner overcome the motherhood penalty.

1. Encourage Collaborative Problem-Solving Sessions

The benefits of collaborative efforts between partners to enhance relationship satisfaction are well-established. If your partner is grappling with challenges stemming from systemic issues like the motherhood penalty, set aside time for joint problem-solving sessions. Approach these sessions as strategic brainstorming endeavors, where both of you work together to devise innovative solutions.

Embrace an open-minded attitude, encouraging curiosity and creativity to explore unconventional ideas and approaches. Your steadfast support can empower your partner to actively engage in finding solutions that align with her unique circumstances.

Moreover, this collaborative endeavor cultivates a sense of partnership and solidarity, strengthening your relationship as you address the systemic barriers impacting her personal and professional life. It offers an opportunity to deepen mutual understanding and reinforce respect, creating a supportive environment where both partners feel valued and heard.

2. Share Household Responsibilities

A study published in the Journal of Family and Economic Issues highlights the gendered dynamics of parenting labor division and its interaction with work preferences. It shows that mothers in dual-earner households experience greater parenting inequalities compared to fathers, even after accounting for housework disparities. This inequality negatively affects relationship quality, especially for mothers, due to perceived unfairness in parenting task allocation. Additionally, part-time working mothers face amplified detrimental effects, as their preferred work hours often differ from their actual hours.

Taking proactive steps to share household and childcare duties with your spouse, including cooking, cleaning and childcare, not only eases her burden but also demonstrates a commitment to equality and partnership.

Collaboratively establishing a fair division of labor, considering each partner’s needs, strengths and commitments, fosters mutual respect and understanding. Sharing of responsibilities also creates a supportive environment that enables your spouse to pursue her career goals with greater focus, knowing that she has your unwavering support at home.

3. Advocate For Workplace Equality

Supporting your wife means actively advocating for workplace policies and practices that uphold gender equality and empower working mothers. Speak out against discriminatory practices and champion initiatives like flexible work arrangements, parental leave policies and equal pay. Research from Stanford University suggests that legal mandates hold promise in addressing the “motherhood penalty.”

By joining forces with your wife in advocating for these important issues, you not only demonstrate your dedication to her well-being but also contribute to creating a more inclusive and supportive work environment for all women. Your advocacy can be a catalyst for change, helping to dismantle systemic barriers and tackle the underlying causes of gender inequality.

Moreover, your active involvement in advocacy sends a powerful message of solidarity to your wife, showing that you stand beside her in the struggle for workplace equality. This shared commitment can inspire positive change within your workplace and community, creating a ripple effect in favor of a culture of support and inclusivity for working mothers.

Is paying the motherhood penalty emptying your cup? Take this test to know if you are inching close to a burnout: Parental Burnout Assessment

Mark Travers

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'There's been almost no talk about the Kamala problem'

Opinion, comment and editorials of the day

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Vice President Kamala Harris speaks during a 'First In The Nation' campaign rally at South Carolina State University on February 02, 2024

'With Biden in mental decline, how do you solve a problem like Kamala Harris?'

Mark Hemingway at The Federalist

With the special counsel's report intensifying attention to President Joe Biden's "age and cognitive decline," Democrats need to discuss "the Kamala problem," says Mark Hemingway at The Federalist. Vice President Kamala Harris is "an almost complete nonentity" policy-wise, but she's still "actively disliked by voters." Democrats won't replace her, but that would be "the smart political move." A running mate "who's able to vigorously campaign could be the difference between Biden's reelection and Trump: The Revenging."

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'The empty promise of endless steak'

Joe Fassler in The New York Times

"Cultured meat" was supposed to save the planet, says Joe Fassler in The New York Times. We were going to have "abundant and affordable" meat — "without the killing" — but use less land and water. We would "drastically cut planet-warming emissions" without depriving ourselves of the "juicy burgers and seared tuna" we love. But years of effort have shown it was "a delicious delusion." Averting "climate catastrophe" is going to take hard work and sacrifice.

'Biden's latest abortion fumble is particularly distressing'

Susan Rinkunas at Slate

President Joe Biden says he doesn't "want abortion on demand" but "thought Roe v. Wade was right," says Susan Rinkunas at Slate. That's "certainly not enough" for a "presidential candidate whose party should be running on abortion access." Right-wingers use the phrase "abortion on demand" to make women seeking abortions "seem flighty." In the real world, "women demand abortions because they need them." They're also "human beings who deserve to make their own choices."

'Trump pretends he's still president. Biden should treat him that way.'

Alex Shepherd in The New Republic

"Donald Trump pretends he's still president," says Alex Shepherd in The New Republic. There's a "perverse kernel of truth" in his fantasy. He wields "unprecedented control" over the Republican Party. The border deal, for example, was "the most restrictive immigration reform in decades" but Republicans "killed it at Trump's behest." If Trump wants to act like an incumbent, President Joe Biden "should humor" him and point out he's bringing back the "chaos" voters "roundly rejected" in 2020.

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Harold Maass is a contributing editor at The Week. He has been writing for The Week since the 2001 debut of the U.S. print edition and served as editor of TheWeek.com when it launched in 2008. Harold started his career as a newspaper reporter in South Florida and Haiti. He has previously worked for a variety of news outlets, including The Miami Herald, ABC News and Fox News, and for several years wrote a daily roundup of financial news for The Week and Yahoo Finance. 

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IMAGES

  1. Math 7 Problem Solving

    to solve age problems

  2. How to solve AGE PROBLEMS the simplest way part1 [Math]

    to solve age problems

  3. How to solve age problem

    to solve age problems

  4. How to Solve Age Problems Part 2

    to solve age problems

  5. Using Equations to Solve Age Problems in Math

    to solve age problems

  6. PPT

    to solve age problems

VIDEO

  1. Age doesn’t matter 1 year age gap

  2. PROBLEM BASED ON AGES

  3. Algebra: How to solve age problem!

  4. AGE PROBLEM 2: How to solve age problems?

  5. Age Problems

  6. EASY WAY TO SOLVE AGE PROBLEMS IN MATH

COMMENTS

  1. Age Word Problems

    Solution: Now that we have the value for [latex]x [/latex], let's find out what Tanya and Marcus's current ages are. We can do this by simply replacing the [latex]x [/latex]'s with [latex]8 [/latex]. CURRENT AGES (present) Marcus: [latex]x = {\textbf {8}} [/latex] years old

  2. Notable & Quotable: Age Problem

    Notable & Quotable: Age Problem 'Since Biden has trouble communicating, he could give greater prominence to Vice President Kamala Harris.' Feb. 16, 2024 4:29 pm ET

  3. 7.9 Age Word Problems

    The last statement gives us the equation to solve: Five years ago, the sum of their ages was 28 (D + 7) + (D − 5) = 28 2D + 2 = 28 − 2 −2 2D = 26 D = 26 2 = 13 ( D + 7) + ( D − 5) = 28 2 D + 2 = 28 − 2 − 2 2 D = 26 D = 26 2 = 13 Therefore, Carmen is David's age (13) + 12 years = 25 years old. Example 7.9.3

  4. Age Problems

    Study Guides Algebra I Age Problems Age Problems Here are some examples for calculating age in word problems. Example 1 Phil is Tom's father. Phil is 35 years old. Three years ago, Phil was four times as old as his son was then. How old is Tom now? First, circle what it is you must ultimately find— how old is Tom now?

  5. Algebra: Age Problems (video lessons, examples, solutions)

    Solution: Step 1: Set up a table. Step 2: Fill in the table with information given in the question. John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now? Let x be Peter's age now. Add 5 to get the ages in 5 yrs.

  6. Learn how to set up and solve 'age' word problems.

    Purplemath What are "age" word problems? "Age" type word problems are those which compare two persons' ages, or one person's ages at different times in their lives, or some combination thereof. Here's an example from my own life: Age Word Problems In January of the year 2000, I was one more than eleven times as old as my son Will.

  7. Age Word Problems (video lessons, examples and solutions)

    Step 1: Let x be John's age now. Look at the question and put the relevant expressions above it. Step 2: Write out the equation. Isolate variable x Answer: John is now 18 years old. How To Use Algebra To Solve Age Problems? Examples: Ten years from now, Orlando will be three times older than he is today. What is his current age?

  8. Age Word Problems In Algebra

    This math tutorial video explains how to solve age word problems in Algebra given the past, present, and future ages of individuals relative to each other. ...

  9. Using Equations to Solve Age Problems in Math

    In mathematics, age problems are easier to solve when transformed into expressions or equations. Learn the steps on how to solve age word problems in math and understand the given examples.

  10. Solving age word problems in Algebra

    Solving age word problems in Algebra — Krista King Math | Online math help Age word problems are like number word problems. You'll still need to relate sentences in English to mathematical equations to solve for people's ages. In this lesson we'll look at how to do that. One helpful way to organize these types of problems is by making a table.

  11. Which came first, the Biden age concerns or the coverage of them?

    Americans are quite aware of Biden's age; polling conducted by YouGov last fall found that 6 in 10 Americans could guess Biden's age to within two years. An 81-year-old embarking on a ...

  12. Lesson Solving Age Problems

    When solving age problems, you need to represent the following in terms of a variable: - the present ages of the people or things involved - the age, at the other specified time, of the people or things involved Then, form an equation based on these representations. Here are some examples:

  13. How to Solve Age Problems Easily

    1.44M subscribers 19K views 6 months ago tecmath math ...more ...more Age problems in maths can be solved easily by combining all the information into a single equation and then solving. Lots...

  14. Lesson Age problems and their solutions

    . Solve this equation by simplifying it step by step: (after brackets opening at the right side) (after moving variable terms to the right and constant terms to the left) (after combining like terms) Thus you got that Kevin's present age is years. Check. If Kevin's present age is 7 years, then Margaret is years old now.

  15. Math Practice Problems

    1. Maria is 12 years old. The sum of the ages of Maria and John is 60. How old is John? 2. Mary is 11 years old. The sum of the ages of Mary and Tiffany is 17. How old is Tiffany? Complexity=5, Mode=Type B Solve the following age problems. 1. 5 years from now Maria will be 34 years old. The current sum of the ages of Maria and Mary is 69.

  16. Age word problem: Ben & William (video)

    Sal solves the following age word problem: William is 4 times as old as Ben. 12 years ago, William was 7 times as old as Ben. How old is Ben now? Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted 1636704 7 years ago

  17. Tricks To Solve Age-Based Problems

    Tricks To Solve Age-Based Problems Read Problems on ages is an important chapter for SSC/Banking and all other exams. In SSC Prelims 2 to 3 questions are asked and in mains 4 to 5 questions can be asked on this topic. As most of the questions on this topic of this chapter can be solved by analytical thinking.

  18. Algebra AGE WORD PROBLEM

    TabletClass Math:https://tcmathacademy.com/ Math help with algebra word problem involving age. For more math help to include math lessons, practice problems...

  19. Why the Age Issue Is Hurting Biden So Much More Than Trump

    Both Donald J. Trump and President Biden are over 75. But voters are much less likely to worry that Mr. Trump is too old to serve. By Rebecca Davis O'Brien Donald J. Trump has praised Hungary ...

  20. Age word problems

    Lesson 6: Systems of equations word problems. Age word problem: Imran. Age word problem: Ben & William. Age word problem: Arman & Diya. Math >. Algebra 1 >. Systems of equations >. Systems of equations word problems.

  21. Equation Problems of Age: Concepts and Practice Questions

    The basic rule is that if the number of unknowns is equal to the number of conditions, then these equations are solvable, otherwise not. We will see some important examples here but first, let us see the following tricks. If the age of a person is 'x', then 'n' years after today, the age = x + n.

  22. How Biden (and Biden Alone) Can Solve His Age Problem

    Biden is behind in polls for reasons he can't change. So he has a critical decision to make: whether to step aside so Democrats can nominate another candidate.

  23. Opinion

    Mr. Biden is the same age as Harrison Ford, Paul McCartney and Martin Scorsese. He's also a bit younger than Jane Fonda (86) and a lot younger than the Berkshire Hathaway C.E.O., Warren Buffett ...

  24. Age and Mixture Problems and Solutions in Algebra

    Problem 1: Father and Son's Ages. Two times the father's age is eight more than six times the son's age. Ten years ago, the sum of their ages was 36 years. The age of the son is: Solution. a. Let x be the age of the son and y be the age of the father.

  25. Algebra Age-Related Word Problem Worksheets

    Steps to Solving the Algebraic Age Word Problem. First, students should combine like terms from the above equation, such as a + 2a (which equals 3a), to simplify the equation to read 3a = 5a - 48. Once they've simplified the equation on either side of the equals sign as much as possible, it's time to use the distributive property of formulas to ...

  26. Age Word Problems: Formula, Solved Examples & FAQs

    There are no specific formulas for age word problems. However, there are some general steps that can be followed to solve age word problems: Step 1: Read the problem carefully and identify the unknowns. Usually, the problem will ask for the age of one or more individuals at a specific point in time. Step 2: Assign variables to represent the ...

  27. A Psychologist Explains How Couples Can Defeat The ...

    A Psychologist Explains The 'New-Age Nostalgia' Trend. Feb 16, 2024, 07:15pm EST. ... Encourage Collaborative Problem-Solving Sessions.

  28. 'There's been almost no talk about the Kamala problem'

    With the special counsel's report intensifying attention to President Joe Biden's "age and cognitive decline," Democrats need to discuss "the Kamala problem," says Mark Hemingway at The Federalist.