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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

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Algebra Topics  - Introduction to Word Problems

Algebra topics  -, introduction to word problems, algebra topics introduction to word problems.

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Algebra Topics: Introduction to Word Problems

Lesson 9: introduction to word problems.

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What are word problems?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?

Johnny has 12 apples. If he gives four to Susie, how many will he have left?

You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:

12 - 4 = 8 , so you know Johnny has 8 apples left.

Word problems in algebra

If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.

You can tackle any word problem by following these five steps:

  • Read through the problem carefully, and figure out what it's about.
  • Represent unknown numbers with variables.
  • Translate the rest of the problem into a mathematical expression.
  • Solve the problem.
  • Check your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.

Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you're reading, consider:

  • What question is the problem asking?
  • What information do you already have?

Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?

There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question.

There are a few important things we know that will help us figure out the total mileage Jada drove:

  • The van cost $30 per day.
  • In addition to paying a daily charge, Jada paid $0.50 per mile.
  • Jada had the van for 2 days.
  • The total cost was $360 .

Step 2: Represent unknown numbers with variables.

In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.

Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember.

Step 3: Translate the rest of the problem.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive?

We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:

$30 per day plus $0.50 per mile is $360.

If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression.

Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .)

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = .

Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.

30 ⋅ 2 + .5 ⋅ m = 360

Now we have our expression. All that's left to do is solve it.

Step 4: Solve the problem.

This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m .

60 + .5m = 360

Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem.

We can start by getting rid of the 60 on the left side by subtracting it from both sides .

The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it.

.5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles.

Step 5: Check the problem.

To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.

According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:

$30 per day and $0.50 per mile

30 ⋅ day + .5 ⋅ mile

30 ⋅ 2 + .5 ⋅ 600

According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!

While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.

Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are:

If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math.

Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps.

A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?

Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?

Problem 1 Answer

Here's Problem 1:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

Answer: $29

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

Step 1: Read through the problem carefully

The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight:

So is the information we'll need to answer the question:

  • A single ticket costs $8 .
  • The family pass costs $25 more than half the price of the single ticket.

Step 2: Represent the unknown numbers with variables

The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f .

Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost?

In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how:

  • First, replace the cost of a family pass with our variable f .

f equals half of $8 plus $25

  • Next, take out the dollar signs and replace words like plus and equals with operators.

f = half of 8 + 25

  • Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ :

f = 1/2 ⋅ 8 + 25

Step 4: Solve the problem

Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.

  • f is already alone on the left side of the equation, so all we have to do is calculate the right side.
  • First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
  • Next, add 4 and 25. 4 + 25 equals 29 .

That's it! f is equal to 29. In other words, the cost of a family pass is $29 .

Step 5: Check your work

Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.

We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.

  • We could translate this into this equation, with s standing for the cost of a single ticket.

1/2s = 29 - 25

  • Let's work on the right side first. 29 - 25 is 4 .
  • To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .

According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!

So now we're sure about the answer to our problem: The cost of a family pass is $29 .

Problem 2 Answer

Here's Problem 2:

Answer: $70

Let's go through this problem one step at a time.

Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here?

To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem:

  • The amount Flor donated is three times as much the amount Mo donated
  • Flor and Mo's donations add up to $280 total

The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m .

Here's the problem again. This time, the important facts are highlighted.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give?

The important facts of the problem could also be expressed this way:

Mo's donation plus Flor's donation equals $280

Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say:

Mo's donation plus three times Mo's donation equals $280

We can translate this into a math problem in only a few steps. Here's how:

  • Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m .

m plus three times m equals $280

  • Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign.

m + three times m = 280

  • Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m .

m + 3m = 280

It will only take a few steps to solve this problem.

  • To get the correct answer, we'll have to get m alone on one side of the equation.
  • To start, let's add m and 3 m . That's 4 m .
  • We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .

We've got our answer: m = 70 . In other words, Mo donated $70 .

The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again.

If our answer is correct, $70 and three times $70 should add up to $280 .

  • We can write our new equation like this:

70 + 3 ⋅ 70 = 280

  • The order of operations calls for us to multiply first. 3 ⋅ 70 is 210.

70 + 210 = 280

  • The last step is to add 70 and 210. 70 plus 210 equals 280 .

280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity.

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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

  • Read the whole thing first
  • Do a sketch if possible
  • Assign letters for the values
  • Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

  • Let S = dollars Sam has
  • Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

  • Let D = number of dogs
  • Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

  • Use w for width of rectangle: w = 12m
  • Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

tennis

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

  • Use S for how many games Sam played
  • Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

table

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

  • Use a for Alex's work rate
  • Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

track

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

  • The number of "5 hour" days: d
  • The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

  • Use A for Area: A = 12 mm 2
  • Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

  • Use V for Volume
  • Use A for Area
  • Use s for side length of cube
  • Volume of a cube: V = s 3
  • Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

pizza

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

  • Joel's normal rate of pay: $N per hour
  • Joel works for 40 hours at $N per hour = $40N
  • When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
  • Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
  • And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

  • Present Value PV = $2,000
  • Interest Rate (as a decimal): r = 0.11
  • Number of Periods: n = 3
  • Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

  • Present Value PV = $1,000
  • Interest Rate (the value we want): r
  • Number of Periods: n = 9
  • Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

  • Number of boys now: b
  • Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

  • We could try, say, n=10: 10(12) = 120 NO (too small)
  • Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

  • the length of the room: L
  • the width of the room: W
  • the total Area including veranda: A
  • the width of the room is half its length: W = ½L
  • the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

Introduction to Word Problems

These lessons, with videos, examples, solutions and worksheets, help Grade 5 students learn how to solve word problems.

Related Pages More Grade 5 Math Word Problems More Lessons for Grade 5 Math Math Worksheets

The following diagram gives some examples of word problems keywords or clue words. Scroll down the page for more examples and solutions of word problems.

Word Problem Keywords

Introduction to Word Problem Terms

Problem Solving Strategies

Explain the meanings of the four basic operations–addition, subtraction, multiplication and division–so that you can understand how to solve word problems correctly.

Helpful hints for solving word problems

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Word Problems Calculators: (41) lessons

2 number word problems.

Free 2 number Word Problems Calculator - This calculator handles word problems in the format below: * Two numbers have a sum of 70 and a product of 1189 What are the numbers? * Two numbers have a sum of 70. Their difference 32

2 Unknown Word Problems

Free 2 Unknown Word Problems Calculator - Solves a word problem based on two unknown variables

Age Difference

Free Age Difference Calculator - Determines the ages for an age difference word problem.

Age Word Problems

Free Age Word Problems Calculator - Determines age in age word problems

Angle of Elevation

Free Angle of Elevation Calculator - Solves angle of elevation word problems

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

Coin Combinations

Free Coin Combinations Calculator - Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

Coin Total Word Problems

Free Coin Total Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another

Coin Word Problems

Free Coin Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value

Collinear Points that form Unique Lines

Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.

Compare Raises

Free Compare Raises Calculator - Given two people with a salary and annual raise amount, this determines how long it takes for the person with the lower salary to catch the person with the higher salary.

Consecutive Integer Word Problems

Free Consecutive Integer Word Problems Calculator - Calculates the word problem for what two consecutive integers, if summed up or multiplied together, equal a number entered.

Cost Revenue Profit

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Free Decay Calculator - Determines decay based on an initial mass and decay percentage and time.

Distance Catch Up

Free Distance Catch Up Calculator - Calculates the amount of time that it takes for a person traveling at one speed to catch a person traveling at another speed when one person leaves at a later time.

Distance Rate and Time

Free Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.

Find two numbers word problems

Free Find two numbers word problems Calculator - Given two numbers with a sum of s where one number is n greater than another, this calculator determines both numbers.

Inclusive Number Word Problems

Free Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions: 1) The Average of all numbers inclusive from A to B 2) The Count of all numbers inclusive from A to B 3) The Sum of all numbers inclusive from A to B

Free Map Scale Calculator - Solves map scale problems based on unit measurements

Markup Markdown

Free Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Numbers Word Problems

Free Numbers Word Problems Calculator - Solves various basic math and algebra word problems with numbers

Free Overtime Calculator - Solves overtime wage problems

Percent Off Problem

Free Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.

Percentage of the Pie Word Problem

Free Percentage of the Pie Word Problem Calculator - This takes two or three fractions of ownership in some good or object, and figures out what remaining fraction is left over.

Percentage Word Problems

Free Percentage Word Problems Calculator - Solves percentage word problems

Population Doubling Time

Free Population Doubling Time Calculator - Determines population growth based on a doubling time.

Population Growth

Free Population Growth Calculator - Determines population growth based on an exponential growth model.

Product of Consecutive Numbers

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include: product of 2 consecutive integers product of 2 consecutive numbers product of 2 consecutive even integers product of 2 consecutive odd integers product of 2 consecutive even numbers product of 2 consecutive odd numbers product of two consecutive integers product of two consecutive odd integers product of two consecutive even integers product of two consecutive numbers product of two consecutive odd numbers product of two consecutive even numbers product of 3 consecutive integers product of 3 consecutive numbers product of 3 consecutive even integers product of 3 consecutive odd integers product of 3 consecutive even numbers product of 3 consecutive odd numbers product of three consecutive integers product of three consecutive odd integers product of three consecutive even integers product of three consecutive numbers product of three consecutive odd numbers product of three consecutive even numbers product of 4 consecutive integers product of 4 consecutive numbers product of 4 consecutive even integers product of 4 consecutive odd integers product of 4 consecutive even numbers product of 4 consecutive odd numbers product of four consecutive integers product of four consecutive odd integers product of four consecutive even integers product of four consecutive numbers product of four consecutive odd numbers product of four consecutive even numbers product of 5 consecutive integers product of 5 consecutive numbers product of 5 consecutive even integers product of 5 consecutive odd integers product of 5 consecutive even numbers product of 5 consecutive odd numbers product of five consecutive integers product of five consecutive odd integers product of five consecutive even integers product of five consecutive numbers product of five consecutive odd numbers product of five consecutive even numbers

Ratio Word Problems

Free Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Slope Word Problems

Free Slope Word Problems Calculator - Solves slope word problems

Solution Mixture

Free Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Sum of Consecutive Numbers

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include: sum of 2 consecutive integers sum of 2 consecutive numbers sum of 2 consecutive even integers sum of 2 consecutive odd integers sum of 2 consecutive even numbers sum of 2 consecutive odd numbers sum of two consecutive integers sum of two consecutive odd integers sum of two consecutive even integers sum of two consecutive numbers sum of two consecutive odd numbers sum of two consecutive even numbers sum of 3 consecutive integers sum of 3 consecutive numbers sum of 3 consecutive even integers sum of 3 consecutive odd integers sum of 3 consecutive even numbers sum of 3 consecutive odd numbers sum of three consecutive integers sum of three consecutive odd integers sum of three consecutive even integers sum of three consecutive numbers sum of three consecutive odd numbers sum of three consecutive even numbers sum of 4 consecutive integers sum of 4 consecutive numbers sum of 4 consecutive even integers sum of 4 consecutive odd integers sum of 4 consecutive even numbers sum of 4 consecutive odd numbers sum of four consecutive integers sum of four consecutive odd integers sum of four consecutive even integers sum of four consecutive numbers sum of four consecutive odd numbers sum of four consecutive even numbers sum of 5 consecutive integers sum of 5 consecutive numbers sum of 5 consecutive even integers sum of 5 consecutive odd integers sum of 5 consecutive even numbers sum of 5 consecutive odd numbers sum of five consecutive integers sum of five consecutive odd integers sum of five consecutive even integers sum of five consecutive numbers sum of five consecutive odd numbers sum of five consecutive even numbers

Sum of Five Consecutive Integers

Free Sum of Five Consecutive Integers Calculator - Finds five consecutive integers, if applicable, who have a sum equal to a number. Sum of 5 consecutive integers

Sum of Four Consecutive Integers

Free Sum of Four Consecutive Integers Calculator - Finds four consecutive integers, if applicable, who have a sum equal to a number. Sum of 4 consecutive integers

Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n) * Whole Numbers * Natural Numbers * Even Numbers * Odd Numbers * Square Numbers * Cube Numbers * Fourth Power Numbers

Sum of Three Consecutive Integers

Free Sum of Three Consecutive Integers Calculator - Finds three consecutive integers, if applicable, who have a sum equal to a number. Sum of 3 consecutive integers

Free Sun Shadow Calculator - This solves for various components and scenarios of the sun shadow problem

Unit Savings

Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.

Work Word Problems

Free Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.

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SOLVING WORD PROBLEMS: A VISUAL APPROACH: HOME

solve the word problems below show your solution

Step 1: Identify the given information in the problem.

Underline the information in your problem. Then create a checklist. As you use the information in your solution, make sure to check off each box.

Understanding a math word problem is 50% of the work. So give yourself a pat on the back when you’ve finished it! 

Step 2: Find the question in the passage and state it in your own words.

Underline the question with a different color than you used for the first step. After you have underlined the question, write the information out in your own words, so that you understand what is being asked. 

Step 3: Devise a strategy to solve the problem.

Now that you have collected the information you need to solve the problem, you need to come up with a strategy to conquer the problem.

Think about what’s being asked. Is there a formula you need to use? Do you need to calculate a percentage for your final answer? Write out the steps you need to use to solve the problem, so that you can carry out your plan.

THE STEPS TO SOLVING A WORD PROBLEM

  • Identify the given information.
  • Find the question and state it in your own words.
  • Devise a strategy to solve the problem.
  • Carry out your plan.

Use three different colored pencils/pens to separate each of the first three parts of the problem solving process.

Here are a few examples of how to use this process in solving a mathematical problem.

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Step 4: Once you have created a plan, then you need to solve the problem. Make sure you have used all the given information in the problem, answered the question, and followed each step in your strategy.

Keep Calm.   Be confident.  You’ve got this! 

solve the word problems below show your solution

  • Last Updated: Nov 22, 2017 12:17 PM
  • URL: https://guides.kendall.edu/wordproblems

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math tutorials for students majoring in the earth sciences

How do I solve math word problems? Breaking down the process to solve math problems in the Earth sciences

Math-Curious child

"Given/Find/Solve/Evaluate" - A systematic approach to solving word or story problems

Your instructor passes out a paper on the first day of class with a half-page paragraph of words and numbers and asks you to solve the problem. This intimidating activity can be especially daunting for a student in a science class that isn't confident in their math skills, especially applying it in a way they've not done before. Add to that the instructor may be assuming students are comfortable with word problems, so doesn't spend time on the basics. How do you proceed as the instructor watches and waits?

Word problems (from middle or high school you may know them as "story" problems) are an important step in student learning because in real-world applications, scientists almost never have information ready to just plug into a formula. It's especially helpful to have a dependable way to approach word problems in science, mostly predicated on careful reading and patience ! The "Given/Find/Solve/Evaluate" strategy (GFSE for our purposes here), is a simple way to slow yourself down and break a word problem into smaller pieces.

The general premise of GFSE is to figure out all of the different variables and values that are in the problem (G) , what you're being asked for (F) , how to set up and complete the problem (S) , and evaluating your answer for correct units and reasonableness of your number (E) .

When do I use GFSE?

Any time you are confronted with a math problem, you should have a trusted, consistent approach to finding a solution. Without it, you might feel overwhelmed every time you have to solve one! Given/Find/Solve/Evaluate is one of a number of related methods that involve breaking down a problem. It is a general approach that can be used in any course or scenario where you need to use math principles.

Rational Solution

How do I use GFSE?

The main thing to keep in mind when using the GFSE approach is to slow yourself down and work through the problem methodically. That might seem obvious or even annoying, because we often want to jump right in to getting something done. However, if you have struggled with word problems in the past, a likely source of some of those struggles is that you missed key pieces of information or misplaced a variable. These problems are reduced as you work deliberately through the steps below. See the example below for an illustration of how this works and the thought processes that go into the solution.

Quillayute,WA rainstorm

GFSE for Unit Conversions

Precipitation across the United States varies a great deal because of the large land area and due to topographic and climatic differences across the country. The National Weather Service reports precipitation in inches but scientists typically use metric. The average annual precipitation for the wettest place in the continental United States is Quillayute, WA, at 99.5 inches, whereas, it is only 2.0 inches in Stovepipe Wells, CA. What is the average annual precipitation in centimeters (cm) and millimeters (mm) at each of these locations?

Step 1. On your paper, start by writing "Given:" After that, list the terms that are given in the problem. For this problem:

`P_w = 99.5 " in"` , `P_d = 2.0 " in"`

Note that the terms `P_w` and `P_d` may seem arbitrary. The truth is that they are! But for now, we need to assign a variable that represents each term. In this case, `P_w` indicates precipitation for the wettest location and `P_d` indicates precipitation for the driest location.

Step 2. Now write "Find" below your "Given" items.  Identify the variable that you are being asked to solve for.  For this problem...

`P_w = ? " cm"` , `P_w = ? " mm"` `P_d = ? " cm"` , `P_d = ? " mm"`

It is important to note that I've included not only the variables but also the UNITS!  Keeping the units in throughout your solution to the problem will help to ensure that you are getting the correct answer.

Also think about what you Know already. You probably have learned about the conversion between inches and cm and mm. To solve this problem, remember there are 2.54 cm to 1 inch (and 25.4 mm to 1 inch).

Step 3 . Write "Solve." Now you'll begin the solution to the problem. Because you may not be familiar with precipitation, you should consider logic and what you DO already know. Consider this, you're already given precipitation values, so you don't need to calculate anything NEW. All you need to do for this problem is to convert the rainfall amounts to the different units!

Mosaic Canyon Cactus

`P_w = 99.5 " in" *((2.54 " cm")/(1 " in")) = 253 " cm"` `P_w = 99.5 " in" *((25.4 " mm")/(1 " in")) = 2527 " mm"` `P_d = 2.0 " in" *((2.54 " cm")/(1 " in")) = 5.1 " cm"` `P_d = 2.0 " in" *((25.4 " mm")/(1 " in")) = 51 " mm"`

This example is pretty simple to solve. Note that all you really need to do is the unit conversion and as you complete the multiplication, the units of inches cancel out.

Step 4. " Evaluate" your answer. If you were asked for specific units, are those the units you finished with? Does your answer make sense?

Helpful Tips

  • Circle, highlight, box out, double-underline, etc. your answers! Make them obvious and easy to find.
  • Including the ZERO in front of a decimal value. 0.45 is correct, .45 is incorrect!
  • Use correct (or at least reasonable) significant figures! An answer of 12.64578329 cm is technically WRONG if you are calculating based on measurements that are not that precise. It's likely 13 cm, 12.6 cm, or 12.65 cm are within the measurement error tolerance. As a general rule, you should use the number of significant figures that the least precise variable in the original problem had.
  • Use scientific notation for large or small values!  In most cases, an answer of 12,345, 000 cm should be reported as 1.23 x 10 7 cm. For more practice with scientific notation, visit the Scientific Notation module . 
  • Use metric system units unless otherwise specified.
  • Spreadsheets and programming can be very powerful tools! As you progress through science, hopefully you will embrace the opportunities to learn the skills to take advantage of them. 

GFSE for Equations

Some topics are too large or small, or take very long or very short time intervals, to be especially precise. In these cases, estimates based on idealized conditions can be used, as long as those assumptions are acknowledged. In the case of volcanoes, the size and shape of the feature are prohibitive of an exact volume calculation. Try this example from Mount St. Helens.

On May 18, 1980, Mount St. Helens erupted, initiated by a large landslide on the north slope. The United States Geological Survey had been measuring earthquake activity and using cameras to monitor the potential for an eruption. Following the eruption, the volcano's shape was completely transformed by the landslide and the evacuation of material from the vent. The original shape of the volcano can be approximated to a CONE.

The diameter of the volcano at the base of Mount St. Helens is approximately 9.7 km, and the pre-eruptive elevation above the base was 2.9 km. How tall in meters was the volcano before the eruption? Calculate an estimate of the volume of Mount St. Helens before the eruption using its pre-eruption geometry in both cubic feet and cubic miles.

Mount St. Helens overlain with cone geometry

Given: `h=2.9" km"` ; `d=9.7" km"`

Find: `h="? " m` ; `V="? " m^3` ; `V="? " km^3`

The volume of a cone is calculated using the equation `V=(1/3)(pi)r^2h` and `1 " km" = 1000 " m"`

Solve: To solve for the height in meters, the calculation is a straightforward unit conversion:

`h=((2.9" km")/1) * ((1000 " m")/(1 " km"))`

`h=2900" m"`

It's helpful to see the problem written out in this way! Notice how the kilometer units are in the numerator in the first term and the denominator in the second term.  It's more obvious when set up like this that the kilometers cancel and you are left with meters in your answer .

In order to calculate the volume in cubic meters, we will also need the diameter in meters:

`h=((9.7 " km")/1) * ((1000 " m")/(1 " km"))`

`h=9700" m"`

Remember that the equation for volume requires the RADIUS (r), but you've been given the DIAMETER (d)!  You should also know that `r = d/2` , so `r = (9700 " m")/2 = 4850 " m"`

The volume calculation in cubic meters using the equation above is:

`V=(1/3)(pi)(4850 " m")^2*2900 "m"`

`V=7.14  "x"  10^10  m^3`

Now, calculate the volume in cubic kilometers.

`V=(1/3)(pi)(4.85 " km")^2*2.9 "km"`

`V=71.4  m^3`

Step 4: Is your answer reasonable?

Yikes, the answer using cubic meters is not particularly helpful. What does ten to the tenth look like? It's really big! So focus on the cubic kilometers answer. A cubic kilometer is one kilometer wide, one kilometer long, and one kilometer high. Mount St. Helens, 9.7 kilometers in diameter and almost 3 kilometers above the local landscape, is a sizable landform, so 71 cubic kilometers is a reasonable estimate.

Who cares? Calculating the pre-eruptive and post-eruptive volumes of the landscape allows scientists to estimate the actual volume of the eruption. Why this might be important? Consider this...if a similar volcano like Mt. Rainier, near Seattle and Tacoma, WA, were to erupt, the predicted volume of the eruption would be especially important for infrastructure and land development, early warning systems, and evacuation planning.

Where do you solve/use GFSE in Earth science?

  • In Hydrology, we are concerned about the interchange of water between the atmosphere, surface water, groundwater, and the oceans.
  • In Volcanology, we calculate hazards based on material viscosity, land slope, eruptive volume, etc.
  • In environmental applications, we may have discontinuous data for soil, water, and human impacts that need to be reconciled.

More help (resources for students)

  • National Council for Special Education: Solving Word Problems in Science and Mathematics ; https://www.sess.ie/sites/default/files/Resources/science/5/5.6_Solving_Word_Problems_in_Science_and_Mathematics.pdf  
  • Khan Academy (https://www.khanacademy.org/) and search "Word Problems"

Pages written by Kyle Fredrick (Pennsylvania Western University - California, PA).

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Solving Systems of Equations Real World Problems

Wow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations . Then we moved onto solving systems using the Substitution Method . In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations.

Now we are ready to apply these strategies to solve real world problems! Are you ready? First let's look at some guidelines for solving real world problems and then we'll look at a few examples.

Steps For Solving Real World Problems

  • Highlight the important information in the problem that will help write two equations.
  • Define your variables
  • Write two equations
  • Use one of the methods for solving systems of equations to solve.
  • Check your answers by substituting your ordered pair into the original equations.
  • Answer the questions in the real world problems. Always write your answer in complete sentences!

Ok... let's look at a few examples. Follow along with me. (Having a calculator will make it easier for you to follow along.)

Example 1: Systems Word Problems

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

1.  Let's start by identifying the important information:

  • hot dogs cost $1.50
  • Sodas cost $0.50
  • Made a total of $78.50
  • Sold 87 hot dogs and sodas combined

2.  Define your variables.

  • Ask yourself, "What am I trying to solve for? What don't I know?

In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually the question at the end will give you this information).

Let x = the number of hot dogs sold

Let y = the number of sodas sold

3. Write two equations.

One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold.

1.50x + 0.50y = 78.50    (Equation related to cost)

 x + y = 87   (Equation related to the number sold)

4.  Solve! 

We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y.

Solving a systems using substitution

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6.  Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7.  Check your work by substituting.

1.50x + 0.50y = 78.50

1.50(35) + 0.50(52) = 78.50

52.50 + 26 = 78.50

35 + 52 = 87

Since both equations check properly, we know that our answers are correct!

That wasn't too bad, was it? The hardest part is writing the equations. From there you already know the strategies for solving. Think carefully about what's happening in the problem when trying to write the two equations.

Example 2: Another Word Problem

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

  • 3 soft tacos + 3 burritos cost $11.25
  • 4 soft tacos + 2 burritos cost $10.00

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25  (Equation representing your lunch)

4x + 2y = 10   (Equation representing your friend's lunch)

We can choose any method that we like to solve the system of equations. I am going to choose the combinations method.

Solving Systems Using Combinations

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You must be able to apply your knowledge!

If you have difficulty with real world problems, you can find more examples and practice problems in the Algebra Class E-course.

Take a look at the questions that other students have submitted:

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Problem about the WNBA

Systems problem about ages

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Telephone Plans problem

Systems problem about hats and scarves

Apples and guavas please!

How much did Alice spend on shoes?

All about stamps

Going to the movies

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

  • System of Equations
  • Systems Word Problems

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Module 9: Multi-Step Linear Equations

Apply a problem-solving strategy to basic word problems, learning outcomes.

  • Practice mindfulness with your attitude about word problems
  • Apply a general problem-solving strategy to solve word problems

 Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

A cartoon image of a girl with a sad expression writing on a piece of paper is shown. There are 5 thought bubbles. They read,

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in the cartoon below. Read the positive thoughts and say them out loud.

A cartoon image of a girl with a confident expression holding some books is shown. There are 4 thought bubbles. They read,

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

  • In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

  • In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

  • Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 6. Check the answer in the problem and make sure it makes sense.

  • We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

  • The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

The top reads,

We list the steps we took to solve the previous example.

Problem-Solving Strategy

  • Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
  • Identify what you are looking for.
  • Name what you are looking for. Choose a variable to represent that quantity.
  • Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
  • Solve the equation using good algebra techniques.
  • Check the answer in the problem. Make sure it makes sense.
  • Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

  • Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
  • Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
  • Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Wordle hints and answer (#968): How to solve the Monday February 12 Wordle

Stuck on today's Wordle word for February 12? Read our hint or find the answer below!

This guide is for a previous day! Looking for today's solution? Check out the Wordle hint and answer for Friday 16th February !

Need a hint for today's Wordle answer? Wordle is an addicting but challenging test of word acumen. Luckily, you're in the right place for some assistance.

Every day, Wordle presents its legions of players with a deviously simple quandary: can you guess the right five-letter word within just six guesses? All you have to help you in finding the Wordle answer are the contextual clues you gain from each guess - but often, that's not enough. Wordle can be tricky, you see, and it's not unusual to look for a little bit of help if you want to preserve your year-long winstreak.

In this guide we'll offer up a selection of Wordle hints to help you figure out today's solution for Monday February 12. Scroll down a bit further and we'll also reveal today's Wordle answer for 12/2.

Use our Wordle Solver tool to help you figure out the answer to any Wordle in moments! Just pop your current guesses in the grid and watch the tool instantly give you all the potential answers.

Wordle hints: Clues for today's Wordle on 12/2

Every day we offer up a number of Wordle hints that you can use to help figure out the solution. So have a read of our clues below and see if you can figure it out before skipping ahead to the answer:

What is the Wordle hint today?

This is a common carbohydrate.

What letter does today's Wordle begin with?

Today's Wordle word begins with P.

What letter does today's Wordle end with?

Today's Wordle word ends with A.

How many vowels are in today's Wordle?

Today's Wordle word contains 2 vowels.

Are there any double letters in today's Wordle?

There are 4 unique letters in today's Wordle word.

What's a good starting word for today's Wordle?

If you type in the starting word "strap", then four letters will turn yellow.

Still having some trouble finding today's Wordle solution? To preserve your win streak, scroll down to reveal today's Wordle answer.

What is today's Wordle answer on February 12?

It's time to reveal the answer to today's Wordle for 12/2. The word is...

Congrats if you managed to correctly guess the Wordle answer today!

How to share your Wordle results without spoilers

A screenshot of the Wordle sharing panel, with the sharing button highlighted and an example on the right of the spoiler-free sharing format which is copied to the clipboard when a user clicks the sharing button.

Wordle has a built-in method of sharing your results in a spoiler-free way, so that those you sent it to don't see today's Wordle word itself, only the colours in your grid to show how well you did.

To share your Wordle results, simply complete (or lose) today's Wordle, and then wait a moment for the statistics panel to appear on your screen. Then tap the "SHARE" button.

On PC this will simply copy the text into your clipboard, so you can then paste the text anywhere you wish, whether it's a private message or a status update on social media. On iPhone or Android, when you tap the "SHARE" button you'll have the option either to copy to clipboard, or to share the results directly to another app on your phone (such as WhatsApp or Twitter).

Using the built-in sharing feature of Wordle is a much nicer way of sharing your results than potentially spoiling the answer to those who haven't yet had the chance to play today's Wordle themselves. So we highly encourage you to use it!

How to play Wordle

Wordle is wonderfully simple. The aim is to guess the correct five-letter word within six guesses. After each guess, the letters of your chosen word will highlight green if they're in the correct place, yellow if they're in the wrong place, or grey if they don't appear in the word at all.

Using these clues you can start to narrow down the correct word. Head over to the Wordle site to try it for yourself!

How did Wordle begin?

Wordle began life as a little family game created by software engineer Josh Wardle. He created the game so that he and his partner could play a fun little word game together during the pandemic, and they quickly realised that there was something quite special in this simple little guessing game. So after a bit of refinement, Wardle released it to the public on his website, Power Language .

The game was released in October 2021, and by the end of the year the game had two million daily players. It became a viral hit, thanks in large part to the ease with which players could share their results in a spoiler-free manner on Twitter and other social media sites. In January 2022, Wardle accepted an offer from the New York Times to acquire Wordle for a seven-figure sum. Well done, Mr Wardle. Well done indeed.

A Wordle grid with punctuation instead of letters for most of the tiles, and a red cross over the whole image.

Are any Wordle words not allowed?

You can type in pretty much any five-letter word in the English language and Wordle will accept it as a guess. However, the answer is picked each day from a much smaller list of more common five-letter words. There are still thousands of possible answers, of course, but it means the answer will never be a word as obscure as, say, "THIOL", or "CAIRD", or "MALIC" (yes, those are all real words).

There are very occasional words which the New York Times will choose not to publish as the day's Wordle answer, perhaps for reasons relating to recent news or politics. For example, shortly after news broke that Roe v Wade might be overturned in the United States, the NYT decided to change the March 30th word from "FETUS" to "SHINE", as the feeling was that the word "fetus" was too politically charged a word in the context of recent events.

The New York Times has also been careful never to allow what they consider to be rude words as the answer to a Wordle puzzle. But of course there's nothing stopping you from using even the dirtiest of words as guesses, as long as they're accepted words in the dictionary, and as long as you realise that they'll never end up being the answer.

Is Wordle getting too easy for you?

If Wordle is starting to get too easy, there are a few ways you can make the game more challenging for yourself. The first choice is to turn on Hard Mode. You can do this on the Wordle site by clicking the cog icon in the top-right of the screen. Hard Mode means that any highlighted letters must be used in all future guesses. This stops you from using the common tactic of choosing two words like "OUNCE" and "PAINS" to test all five vowels early on.

You can take it up another notch by playing by what we call "Ultra-Hard" rules. This means that every guess you enter must potentially be the answer. If you were just playing on Hard Mode, and you typed "MOIST", and the "O" appeared yellow, then nothing would stop you from making "POLAR" as your next word, even though it couldn't possibly be the answer because you already know the "O" is in the wrong place. If you play by "Ultra-Hard" rules, that's not allowed. You must adhere to every clue, and make sure every single word you enter is potentially the answer.

If after all that Wordle is still too easy for you, then you could always try one of the many other Wordle-inspired games online that have cropped up over the past year. One of our favourites is Worldle , in which you must guess a country of the world based on its shape. There's also Waffle , which is about swapping letters in a completed grid to complete all the words; Moviedle , which shows you an entire movie in a tiny space of time and challenges you to guess the movie within six guesses; and Quordle , which tasks you with solving four Wordles at once with the same guesses.

If you need some help with future Wordles, be sure to check out our list of the best Wordle starting words for the greatest chance of success. You can also check out our archive of past Wordle answers to see which words have been chosen previously.

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COMMENTS

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  3. Algebraic word problems

    To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer. It's important for us to keep in mind how we define our variables.

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    Step-by-Step Solutions with Pro Get a step ahead with your homework Go Pro Now. solving word problems. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Examples for Mathematical Word Problems. Word Problems. Solve a word problem: Rachel has 17 apples. She gives 9 to Sarah. How many apples does Rachel have now?

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    Here's how: First, replace the cost of a family pass with our variable f. f equals half of $8 plus $25. Next, take out the dollar signs and replace words like plus and equals with operators. f = half of 8 + 25. Finally, translate the rest of the problem. Half of can be written as 1/2 times, or 1/2 ⋅ : f = 1/2 ⋅ 8 + 25.

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    Solving Word Questions With LOTS of examples! In Algebra we often have word questions like: Example: Sam and Alex play tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play? How do we solve them? The trick is to break the solution into two parts: Turn the English into Algebra.

  10. Word Problems (examples, solutions, videos, worksheets, games, activities)

    Helpful hints for solving word problems. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page.

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    Word Problems Calculator 1-800-234-2933 [email protected] Word Problems Calculators: (41) lessons If you cannot find what you need, post your word problem in our Free 2 number Word Problems Calculator - This calculator handles word problems in the format below: * Two numbers have a sum of 70 and a product of 1189 What are the numbers?

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  13. Solving Word Problems: Steps & Examples

    Step 1: Visualize the Problem. The first step is to visualize the problem. See if you can picture what is going on. Draw pictures if that will help you. Pinpoint or highlight the important parts ...

  14. SOLVING WORD PROBLEMS: A VISUAL APPROACH: HOME

    THE STEPS TO SOLVING A WORD PROBLEM. Identify the given information. Find the question and state it in your own words. Devise a strategy to solve the problem. Carry out your plan. Use three different colored pencils/pens to separate each of the first three parts of the problem solving process.

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    On your paper, start by writing "Given:" After that, list the terms that are given in the problem. For this problem... Step 2. Now write "Find" below your "Given" items. Identify the variable that you are being asked to solve for. For this problem... Step 3. Write "Solve." Now you'll begin the solution of the problem.

  17. Solving Systems of Equations Word Problems

    Wow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations . Then we moved onto solving systems using the Substitution Method. In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations.

  18. Apply a Problem-Solving Strategy to Basic Word Problems

    Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers. Write the equation. 18= 1 2p 18 = 1 2 p. Multiply both sides by 2. 2⋅18=2⋅ 1 2p 2 ⋅ 18 = 2 ⋅ 1 2 p. Simplify. 36=p 36 = p. Step 6. Check the answer in the problem and make sure it makes sense.

  19. Word Problems: Solve Numerical Problems

    Steps for Solving a Word Problem: To work out any word problem, follow the steps given below: 1. Read the Problem: First, read through the problem once. 2. Highlight Facts: Then, read through the problem again and underline or highlight important facts such as numbers or words that indicate an operation. 3.

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  24. Wordle hint and answer for Monday, February 12

    Wordle has a built-in method of sharing your results in a spoiler-free way, so that those you sent it to don't see today's Wordle word itself, only the colours in your grid to show how well you did. To share your Wordle results, simply complete (or lose) today's Wordle, and then wait a moment for the statistics panel to appear on your screen ...