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How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

How to Solve Percent Problems? (+FREE Worksheet!)

Related Topics

  • How to Find Percent of Increase and Decrease
  • How to Find Discount, Tax, and Tip
  • How to Do Percentage Calculations
  • How to Solve Simple Interest Problems

Step by step guide to solve percent problems

  • In each percent problem, we are looking for the base, or part or the percent.
  • Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=2.5 \ ÷ \ 20=0.125=12.5\%\)

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Percent problems – example 2:.

\(40\) is \(10\%\) of what number?

Use the following formula: Base \(= \color{ black }{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=40 \ ÷ \ 0.10=400\) \(40\) is \(10\%\) of \(400\).

Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

In this problem, we are looking for the percent. Use the following equation: \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base \(→\) Percent \(=1.2÷24=0.05=5\%\)

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Percent problems – example 4:.

\(20\) is \(5\%\) of what number?

Use the following formula: Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(→\) Base \(=20÷0.05=400\) \( 20\) is \(5\%\) of \(400\).

Exercises for Calculating Percent Problems

Solve each problem..

  • \(51\) is \(340\%\) of what?
  • \(93\%\) of what number is \(97\)?
  • \(27\%\) of \(142\) is what number?
  • What percent of \(125\) is \(29.3\)?
  • \(60\) is what percent of \(126\)?
  • \(67\) is \(67\%\) of what?

Download Percent Problems Worksheet

  • \(\color{blue}{15}\)
  • \(\color{blue}{104.3}\)
  • \(\color{blue}{38.34}\)
  • \(\color{blue}{23.44\%}\)
  • \(\color{blue}{47.6\%}\)
  • \(\color{blue}{100}\)

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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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Percentages Worksheets

Welcome to the percentages math worksheet page where we are 100% committed to providing excellent math worksheets. This page includes Percentages worksheets including calculating percentages of a number, percentage rates, and original amounts and percentage increase and decrease worksheets.

As you probably know, percentages are a special kind of decimal. Most calculations involving percentages involve using the percentage in its decimal form. This is achieved by dividing the percentage amount by 100. There are many worksheets on percentages below. In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

Most Popular Percentages Worksheets this Week

Calculating the Percent Value of Decimal Currency Amounts and Select Percents

Percentage Calculations

solving percent problems using equations worksheet

Calculating the percentage value of a number involves a little bit of multiplication. One should be familiar with decimal multiplication and decimal place value before working with percentage values. The percentage value needs to be converted to a decimal by dividing by 100. 18%, for example is 18 ÷ 100 = 0.18. When a question asks for a percentage value of a number, it is asking you to multiply the two numbers together.

Example question: What is 18% of 2800? Answer: Convert 18% to a decimal and multiply by 2800. 2800 × 0.18 = 504. 504 is 18% of 2800.

  • Calculating the Percentage Value (Whole Number Results) Calculating the Percentage Value (Whole Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Number Results) (Select percents) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Number Results) Calculating the Percentage Value (Decimal Number Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Number Results) (Select percents) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Number Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Whole Dollar Results) Calculating the Percentage Value (Whole Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Whole Dollar Results) (Select percents) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Whole Dollar Results) (Percents that are multiples of 25%)
  • Calculating the Percentage Value (Decimal Dollar Results) Calculating the Percentage Value (Decimal Dollar Results) (Percents from 1% to 99%) Calculating the Percentage Value (Decimal Dollar Results) (Select percents) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 5%) Calculating the Percentage Value (Decimal Dollar Results) (Percents that are multiples of 25%)

Calculating what percentage one number is of another number is the second common type of percentage calculation. In this case, division is required followed by converting the decimal to a percentage. If the first number is 100% of the value, the second number will also be 100% if the two numbers are equal; however, this isn't usually the case. If the second number is less than the first number, the second number is less than 100%. If the second number is greater than the first number, the second number is greater than 100%. A simple example is: What percentage of 10 is 6? Because 6 is less than 10, it must also be less than 100% of 10. To calculate, divide 6 by 10 to get 0.6; then convert 0.6 to a percentage by multiplying by 100. 0.6 × 100 = 60%. Therefore, 6 is 60% of 10.

Example question: What percentage of 3700 is 2479? First, recognize that 2479 is less than 3700, so the percentage value must also be less than 100%. Divide 2479 by 3700 and multiply by 100. 2479 ÷ 3700 × 100 = 67%.

  • Calculating the Percentage a Whole Number is of Another Whole Number Calculating the Percentage a Whole Number is of Another Whole Number (Percents from 1% to 99%) Calculating the Percentage a Whole Number is of Another Whole Number (Select percents) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Whole Number is of Another Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Number is of a Whole Number Calculating the Percentage a Decimal Number is of a Whole Number (Percents from 1% to 99%) Calculating the Percentage a Decimal Number is of a Whole Number (Select percents) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 5%) Calculating the Percentage a Decimal Number is of a Whole Number (Percents that are multiples of 25%)
  • Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Select percents) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Whole Dollar Amount is of Another Whole Dollar Amount (Percents that are multiples of 25%)
  • Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents from 1% to 99%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Select percents) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 5%) Calculating the Percentage a Decimal Dollar Amount is of a Whole Dollar Amount (Percents that are multiples of 25%)

The third type of percentage calculation involves calculating the original amount from the percentage value and the percentage. The process involved here is the reverse of calculating the percentage value of a number. To get 10% of 100, for example, multiply 100 × 0.10 = 10. To reverse this process, divide 10 by 0.10 to get 100. 10 ÷ 0.10 = 100.

Example question: 4066 is 95% of what original amount? To calculate 4066 in the first place, a number was multiplied by 0.95 to get 4066. To reverse this process, divide to get the original number. In this case, 4066 ÷ 0.95 = 4280.

  • Calculating the Original Amount from a Whole Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Whole Numbers ) Calculating the Original Amount (Select percents) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Whole Numbers )
  • Calculating the Original Amount from a Decimal Number Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Decimals ) Calculating the Original Amount (Select percents) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Decimals )
  • Calculating the Original Amount from a Whole Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Calculating the Original Amount from a Decimal Dollar Result and a Percentage Calculating the Original Amount (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Select percents) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Calculating the Original Amount (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )
  • Mixed Percentage Calculations with Whole Number Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Whole Numbers )
  • Mixed Percentage Calculations with Decimal Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Decimals ) Mixed Percentage Calculations (Select percents) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Decimals )
  • Mixed Percentage Calculations with Whole Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Whole Numbers ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Whole Numbers )
  • Mixed Percentage Calculations with Decimal Dollar Percentage Values Mixed Percentage Calculations (Percents from 1% to 99%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Select percents) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 5%) ( Dollar Amounts and Decimals ) Mixed Percentage Calculations (Percents that are multiples of 25%) ( Dollar Amounts and Decimals )

Percentage Increase/Decrease Worksheets

solving percent problems using equations worksheet

The worksheets in this section have students determine by what percentage something increases or decreases. Each question includes an original amount and a new amount. Students determine the change from the original to the new amount using a formula: ((new - original)/original) × 100 or another method. It should be straight-forward to determine if there is an increase or a decrease. In the case of a decrease, the percentage change (using the formula) will be negative.

  • Percentage Increase/Decrease With Whole Number Percentage Values Percentage Increase/Decrease Whole Numbers with 1% Intervals Percentage Increase/Decrease Whole Numbers with 5% Intervals Percentage Increase/Decrease Whole Numbers with 25% Intervals
  • Percentage Increase/Decrease With Decimal Number Percentage Values Percentage Increase/Decrease Decimals with 1% Intervals Percentage Increase/Decrease Decimals with 5% Intervals Percentage Increase/Decrease Decimals with 25% Intervals
  • Percentage Increase/Decrease With Whole Dollar Percentage Values Percentage Increase/Decrease Whole Dollar Amounts with 1% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 5% Intervals Percentage Increase/Decrease Whole Dollar Amounts with 25% Intervals
  • Percentage Increase/Decrease With Decimal Dollar Percentage Values Percentage Increase/Decrease Decimal Dollar Amounts with 1% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 5% Intervals Percentage Increase/Decrease Decimal Dollar Amounts with 25% Intervals

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Mathematics LibreTexts

5.2.1: Solving Percent Problems

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  • Page ID 62169

  • The NROC Project

Learning Objectives

  • Identify the amount, the base, and the percent in a percent problem.
  • Find the unknown in a percent problem.

Introduction

Percents are a ratio of a number and 100, so they are easier to compare than fractions, as they always have the same denominator, 100. A store may have a 10% off sale. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off. Interest rates on a saving account work in the same way. The more money you put in your account, the more money you get in interest. It’s helpful to understand how these percents are calculated.

Parts of a Percent Problem

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off the original $220 price.

Problems involving percents have any three quantities to work with: the percent , the amount , and the base .

  • The percent has the percent symbol (%) or the word “percent.” In the problem above, 15% is the percent off the purchase price.
  • The base is the whole amount. In the problem above, the whole price of the guitar is $220, which is the base.
  • The amount is the number that relates to the percent. It is always part of the whole. In the problem above, the amount is unknown. Since the percent is the percent off , the amount will be the amount off of the price.

You will return to this problem a bit later. The following examples show how to identify the three parts: the percent, the base, and the amount.

Identify the percent, amount, and base in this problem.

30 is 20% of what number?

Percent: The percent is the number with the % symbol: 20%.

Base : The base is the whole amount, which in this case is unknown.

Amount: The amount based on the percent is 30.

Percent=20%

Base=unknown

The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?

Identify the percent, base, and amount in this problem:

What percent of 30 is 3?

The percent is unknown, because the problem states " What percent?" The base is the whole in the situation, so the base is 30. The amount is the portion of the whole, which is 3 in this case.

Solving with Equations

Percent problems can be solved by writing equations. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.

Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.

The percent of the base is the amount.

Percent of the Base is the Amount.

\[\ \text { Percent } {\color{red}\cdot}\text { Base }{\color{blue}=}\text { Amount } \nonumber \]

In the examples below, the unknown is represented by the letter \(\ n\). The unknown can be represented by any letter or a box \(\ \square\) or even a question mark.

Write an equation that represents the following problem.

\(\ 20 \% \cdot n=30\)

Once you have an equation, you can solve it and find the unknown value. To do this, think about the relationship between multiplication and division. Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Multiplication and division are inverse operations. What one does to a number, the other “undoes.”

When you have an equation such as \(\ 20 \% \cdot n=30\), you can divide 30 by 20% to find the unknown: \(\ n=30 \div 20 \%\).

You can solve this by writing the percent as a decimal or fraction and then dividing.

\(\ n=30 \div 20 \%=30 \div 0.20=150\)

What percent of 72 is 9?

\(\ 12.5 \% \text { of } 72 \text { is } 9\).

You can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.

\(\ 10 \% \text { of } 72=0.1 \cdot 72=7.2\)

\(\ 20 \% \text { of } 72=0.2 \cdot 72=14.4\)

Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.

What is 110% of 24?

\(\ 26.4 \text { is } 110 \% \text { of } 24\).

This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.

18 is what percent of 48?

  • \(\ 0.375 \%\)
  • \(\ 8.64 \%\)
  • \(\ 37.5 \%\)
  • \(\ 864 \%\)

Incorrect. You may have calculated properly, but you forgot to move the decimal point when you rewrote your answer as a percent. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Incorrect. You may have used \(\ 18\) or \(\ 48\) as the percent, rather than the amount or base. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Correct. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives \(\ 37.5 \%\).

Incorrect. You probably used 18 or 48 as the percent, rather than the amount or base, and also forgot to rewrite the percent as a decimal before multiplying. The equation for this problem is \(\ n \cdot 48=18\). The corresponding division is \(\ 18 \div 48\), so \(\ n=0.375\). Rewriting this decimal as a percent gives the correct answer, \(\ 37.5 \%\).

Using Proportions to Solve Percent Problems

Percent problems can also be solved by writing a proportion. A proportion is an equation that sets two ratios or fractions equal to each other. With percent problems, one of the ratios is the percent, written as \(\ \frac{n}{100}\). The other ratio is the amount to the base.

\(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\)

Write a proportion to find the answer to the following question.

30 is 20% of 150.

18 is 125% of what number?

  • \(\ 0.144\)
  • \(\ 694 \frac{4}{9}\) (or about \(\ 694.4\))

Incorrect. You probably didn’t write a proportion and just divided 18 by 125. Or, you incorrectly set up one fraction as \(\ \frac{18}{125}\) and set this equal to the base, \(\ n\). The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Correct. The percent in this case is 125%, so one fraction in the proportion should be \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably put the amount (18) over 100 in the proportion, rather than the percent (125). Perhaps you thought 18 was the percent and 125 was the base. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Incorrect. You probably confused the amount (18) with the percent (125) when you set up the proportion. The correct percent fraction for the proportion is \(\ \frac{125}{100}\). The base is unknown and the amount is 18, so the other fraction is \(\ \frac{18}{n}\). Solving the proportion \(\ \frac{125}{100}=\frac{18}{n}\) gives \(\ n=14.4\).

Let’s go back to the problem that was posed at the beginning. You can now solve this problem as shown in the following example.

Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price .

The coupon will take $33 off the original price.

You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, find these numbers.

\(\ \begin{array}{l} 10 \% \text { of } 220=0.1 \cdot 220=22 \\ 20 \% \text { of } 220=0.2 \cdot 220=44 \end{array}\)

The answer, 33, is between 22 and 44. So $33 seems reasonable.

There are many other situations that involve percents. Below are just a few.

Evelyn bought some books at the local bookstore. Her total bill was $31.50, which included 5% tax. How much did the books cost before tax?

The books cost $30 before tax.

Susana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?

Since 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as, “Susana worked 100% of the hours she worked last week, as well as 75% more.”)

Percent problems have three parts: the percent, the base (or whole), and the amount. Any of those parts may be the unknown value to be found. To solve percent problems, you can use the equation, \(\ \text { Percent } \cdot \text { Base }=\text { Amount }\), and solve for the unknown numbers. Or, you can set up the proportion, \(\ \text { Percent }=\frac{\text { amount }}{\text { base }}\), where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion.

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Percentage Equations Worksheets

There are many times we will need to report or quantify the amount of a whole value something is. The percent equation allows us to do this. The percent equation simple states that the part (a) is to the product of the percent (p) and whole (b). It can be symbolized by a = p x b. While this may seem like a simple algebraic equation it has a huge number of uses and application to real world everyday situations. It is used in all types of game theory to calculate the success and failure of youth to professional levels of just about anything. You can use this to determine how much of a tip you should leave for someone who provided you with great service. The finance industry uses it to determine your monthly bills for loans and credit cards. This selection of worksheets will help you become comfortable using the percentage equation in simple to intermediate level applications.

Aligned Standard: Ratios & Proportional Relationships

  • Piggy Pete's Car Lot Lesson - Piggy Pete owns a car lot that has 80 cars on it. All the cars are the same make and model. He has a sales force of 5 people. Over the course of the month, the sales force sells 60% of the cars on the lot. They sell the cars for $18,500 each. 1. How many cars did they sell in that month? 2. How much money did they make that month?
  • Guided Lesson - You will work on simple problems and apply the equation to complex word problems.
  • Guided Lesson Explanation - You will be shown how to break each of these problems down into a digestible form for yourself.
  • Worksheet 1 - Use a proportion to solve each problem. Round answers to nearest hundredth.
  • Worksheet 2 - This is a mix of simple problems and word problems.
  • Worksheet 3 - There are 800 students at Smith Elementary. The table shows the number or percent of students in each grade. Work off of those values to answer these problems.
  • Worksheet 4 - It is all about selling these specific types of berries.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

These sheets cover the most basic form of question to advanced and complex forms.

  • Homework 1 - 4 is what % less than 80?
  • Homework 2 - The equation that we use for percentage decrease is: difference of values/ larger value x 100%
  • Homework 3 - For all of the problems we need to determine the percentage decrease.
  • Homework 4 - Sam and Bob made $50 painting the fence. If they put in a savings account and want to have $55 at the end of a year, what interest rate would they want to bank to pay?
  • Homework 5 - There are about 8 billion people in the world. About 51% of them are female. How many people are female? (Round to nearest billion)

Practice Worksheets

Each of these sheets get more difficult as you move on.

  • Practice 1 - Solve for what each math sentence is asking you for.
  • Practice 2 - A company surveyed 5000 people to find their favorite music. Fill in the missing values on the chart.
  • Practice 3 - Smithville Paper Co. pays employees on straight commission at a 3% rate. If Bill says $700 worth of paper how much would he make?
  • Practice 4 - At North High School the enrollment is 2000 students. Of those 35% are taking Spanish I and 20% are taking Spanish II. How many students are enrolled in either Spanish I or Spanish II classes?

Math Skill Quizzes

It is time to see how well you are doing with this skill.

  • Quiz 1 - Use a proportion to solve each problem.
  • Quiz 2 - Bill took a poll of two hundred and fifty of his classmates to determine what pet they liked most. The results are shown in the table, but some of it is empty.
  • Quiz 3 - At the end of the three years in the problem above, Carl takes all of his money (interest and investment) and moves it to a savings account that yields 2% interest / year. How much will he make on the investment in that year?
  • Quiz 4 - Bill buys a computer and pays 3% sales tax. If his receipt shows taxes of $60 how much was the computer?

Word Problem and Table Based Sheets

Break all of these down into simple parts and then see how the parts interact before trying to solve them.

  • Word Problems 1 - Use a proportion to solve each problem.
  • Word Problems 2 - One hundred dollars invested at 3% annually for 3.5 years would yield how much interest?
  • Word Problems 3 - Very simple problems that you will need to piece together.
  • Tables 1 - Example: John can select two options of payment. Option A is a commission of 4% and Option B is to be paid $8 per hour. If John thinks he can sell $5000 worth of product and he plans to work 5 hours for 5 days which option would be the best?
  • Tables 2 - What would the discount and final price be on the following sale with a coupon?
  • Tables 3 - We will work this through a whole bunch of financial based problems.

Skills Review Sheets

These are the core skills that are required to solve those story based problems.

  • Review 1 - Pete the Pirate's has 300 pirate friends. If 35% of those are captains of ships, how many captains are there in the group?
  • Review 2 - The next night Michelle meets a group of friends for pizza and brings a 30% off coupon. If the group spends a total of $60 on pizza, how much will Michelle's coupon save the group?
  • Review 3 - At Crest High School 20% of the students are Seniors. If there are 500 students, how many are seniors?
  • Of Over Is Problems Sheet 1 - Use a proportion to solve each problem. Round answers to nearest hundredth.
  • OOI Sheet 2 - Fill in whatever may be missing.
  • OOI Sheet 3 - You will apply that famous equation one more time.
  • OOI Sheet 4 - See how quick you can get through this last one.

How to Calculate Percentage Increases or Decreases

When we are working on something and hoping to improve it or track how far it is falling for its goal. The percentage equations are key. You just need to determine the key metric(s) that indicate success or failure in your project. Then you need to keep an eye on the change in those metrics over a set period of time. Based on the nature of that metric this can be evaluated weekly, monthly, quarterly, or even annually. The function is to track the change (increase or decrease). One of the easiest to make sense of is the change is to see if there was growth or decay within that metric is to compare the figures and see if there was a percentage increase, decrease, or did it remain the same. This is quick three step process:

Step 1: Find the Difference - Look at you’re the starting value and compare it to the latest value. Note if it increased (grew) or decreased (fell).

Step 2: Divide - Divide the latest value by the original. If you noted in step that there was an increase, it is a positive value. If you noted a decrease, it is a negative value.

Step 3 : Multiply by 100 - Multiply the value in step 2 by 100. Add a percentage symbol after it.

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Solving Percent Application Problems

Math: basic tutorials : solving percent application problems.

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Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem.

Example and Activity

What is the sale price of a coat that is normally 95 dollars and is discounted by 20 percent.

Line 1: What are you being asked to find. We are being asked to find the sale price.

Line 2: Choose a variable to represent it. Let s be the sale price.

Line 3: Write a sentence that gives the information to write an equation to find s. If the discount is 20 percent, this means the sale price is 80 percent of the original price.

Line 4: Translate the words into algebra, so the equation is s equals 0 decimal 8 0 times 95.

Line 5: Multiply to solve for s, so s equals 76.

Line 6: Write a statement that answers the question. The sale price of the coat is 76 dollars.

A cupcake contains 480 calories, and 240 of those calories are from fat. What percent of the total calories come from fat?

Line 1: What are you being asked to find? We are being asked to find the percent of the calories that from fat.

Line 2: Choose a variable to represent it. Let p be the percent from fat.

Line 3: Write a sentence that gives the information to find p. What percent of 480 is 240?

Line 4: Translate the words into algebra, so the equation is p time 480 equals 240.

Line 5: Divide both sides of the equation by 480 to solve for p, so the equation is 480p divided by 480 equals 240 divided by 480.

Line 6: Simplify to get p equals 0 decimal 5.

Line 5: Convert the decimal to a percent by multiplying by 100 percent so p = 50 percent.

Line 7: Write a statement that answers the question. Therefore, 50 percent of the calories in the cupcake are from fat.

Source: " Prealgebra - opens in a new window " by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Try this activity to test your skills. If you have trouble, check out the information in the module for help.

Summary and Worksheet

  • Summary: Solving Percent Application Problems - PDF - Opens in a new window This document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
  • Worksheet: Solving Percent Application Problems - PDF - Opens in a new window This document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
  • << Previous: Simple Operations with Percent
  • Next: Solving Percent Change Problems >>

Note: This material is meant as a general guide, if your professor's instructions differ from the information we've provided, always follow your professor's instructions. Also note, icons on this site are used through a Noun Project Pro license. Please be sure to provide proper attribution if you reuse them.

  • Last Updated: Aug 22, 2023 3:28 PM
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Percent Worksheets

This ensemble of printable percentage worksheets is tailor-made for students of grade 6, grade 7, and grade 8. A plethora of exercises like finding the percent of the shaded region, finding percent of a whole numbers and decimals, comparing quantities, well-researched word problems and a lot more are available here. The pdf worksheets are split into metric and customary units to enable convenient downloads. Access some of these worksheets for free!

» Profit and Loss

» Discount

» Simple Interest

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Percent of the Shaded Region: Blocks

Percent of the Shaded Region: Blocks

Engage in this series of base 10 blocks worksheets that contain nine problems per page. Discern and count the shaded squares to determine the percentage of the shaded area.

  • Download the set

Percent of the Shaded Region: Shapes

Percent of the Shaded Region: Shapes

Keenly observe the shaded region of the shapes provided. Find the percentage of the shaded area in each problem.

Percent of a Whole Number

Percent of a Whole Number

Each 6th grade worksheet contains 14 problems calculating the percentage of whole numbers. Use the answer keys to verify your responses.

Percent: Units of Measurement with Word Problems

Percent: Units of Measurement with Word Problems

Calculate the amount for each base value in these worksheets that contain units of measurement. Also, solve the percent word problems based on interesting real-life scenarios.

Percent of a Decimal Number

Percent of a Decimal Number

Find the value that constitutes an equivalent percentage for each decimal and round them to the nearest hundredth.

Comparing Quantities: with Word Problems

Comparing Quantities: with Word Problems

Work out the percentages. Then, compare them and insert the appropriate <, > or = symbols in the boxes. Word problems are also furnished to help learners grasp the concept of comparing quantities.

Percent on a Number Line

Percent on a Number Line

Based on the number line models provided, fill in the boxes with either the appropriate percentages or numbers. These printable worksheets form a great visual aid for 6th grade and 7th grade students in understanding percentages.

Find the Value of the Unknowns

Find the Value of the Unknowns

Read each question carefully to find the unknown percentages, base values or amounts. Round your answers to the nearest hundredth.

Percent of Increase or Decrease: with Word Problems

Percent of Increase or Decrease: with Word Problems

Based on the original amount, find the ratio of change in quantity. Then, calculate the percentage of increase or decrease. Each worksheet includes a number of word problems suitable for 7th grade and 8th grade students.

Find the New Amount: Percent of Increase or Decrease

Find the New Amount: Percent of Increase or Decrease

Find the increase or decrease in amount using the given percentage. Add or subtract the amount so derived to determine the change in quantity. A few word problems are incorporated here for variety.

Percent Error

Percent Error

There's no room for error in our enigmatic pdf worksheets on calculating the percent error in an estimate! Practice finding the difference between a guess and the exact value in the form of percentage in this section.

Convert between Fractions, Decimals, Percent Worksheets

Convert between Fractions, Decimals, Percent Worksheets

Engage this set of printable worksheets that include an assortment of exercises based on conversion between fractions, decimals and percent.

(30 Worksheets)

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Solving Percent Problems using Algebra

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SOLVING PERCENT EQUATIONS WORKSHEET

Problem 1 : 

Solve for x : 

20% of x is 16

Problem 2 : 

x% of 18x is 0.9

Problem 3 : 

15% of 50 is x

Problem 4 : 

If 5 more than 10 percent of x is 85, then  find the value of x. 

Problem 5 : 

If 10 less than 8 percent of x is 26, then  find the value of x. 

Problem 6 : 

Sum of x and y is 150. Sum of 5 percent of x and 10 percent of y is 11. Find the values of x and y 

solving percent problems using equations worksheet

Detailed Answer Key

Solution : 

0.2x  =  16

Divide each side by 0.2

x  =  80

x% of 18 is 0.9

0.01x  ⋅ 18  =  0.9

0.18x  =  0.9

Divide each side by 0.18

x  =  5

0.15  ⋅ 50  =  x

7.5  =  x

5 more than 10 percent of x is 85

10% of x + 5  =  85

0.1x + 5  =  85

Subtract 5 from each side. 

0.1x  =  80

Divide each side by 0.1

x  =  800

10 less than 8 percent of x is 26

8% of x - 10  =  26

0.08x - 10  =  26

Add 10 to each side. 

0.08x  =  36

Divide each side by 0.08

x  =  450

Given :  Sum of x and y is 150.

Then, we have 

x + y  =  150

Subtract y from each side. 

x  =  150 - y -----(1)

Given :  Sum of 5 percent of x and 10 percent of y is 11.

5% of x + 10% of y  =  11

0.05x + 0.1y  =  11

To get rid of the decimals, multiply each side by 100. 

5x + 10y  =  1100

Divide each side by 5.

x + 2y  =  220

From (1), substitute (150 - y) for x.

150 - y + 2y  =  220

150 + y  =  220

Subtract 150 from each side. 

y  =  70

Substitute 70 for y in (1). 

(1)-----> x  =  150 - 70

So, the values of x and y are 80 and 70 respectively.

solving percent problems using equations worksheet

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Solving Percent Problems With Equations

Solving Percent Problems With Equations - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Solve each round to the nearest tenth or tenth of, Percent word problems, Percents, Handouts on percents 2 percent word, Pre activity solving percent problems preparation, Solving proportions date period, Word problem practice workbook, Solving multi step equations.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Solve each problem. Round to the nearest tenth or tenth of ...

2. percent word problems, 3. percents, 4. handouts on percentspage 2 percent word ..., 5. pre-activity solving percent problems preparation, 6. solving proportions date period, 7. word problem practice workbook, 8. solving multi-step equations -.

IMAGES

  1. Worksheet: Percent Problems

    solving percent problems using equations worksheet

  2. Percent Proportion Worksheet by April Langelett

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  3. PPT

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  4. How To Do Math Percentage Problems

    solving percent problems using equations worksheet

  5. Solving Percent Word Problems with Equations

    solving percent problems using equations worksheet

  6. SOLVING PERCENT PROBLEMS USING EQUATIONS by Teacher Deb Egizi

    solving percent problems using equations worksheet

VIDEO

  1. Solving Percent Problems

  2. Changing Percent Question into an Equation

  3. Percent Trick...in Seconds

  4. Solving Percent Problems

  5. Ch E2 & E3 Solving percent problems with EQUATIONS

  6. FREE Percent and Decimal Review Worksheet

COMMENTS

  1. Free Worksheets

    Download over 20,000 K-8 worksheets covering math, reading, social studies, and more. Discover learning games, guided lessons, and other interactive activities for children.

  2. PDF Name [PACKET 4.3: SOLVING PERCENT PROBLEMS ] 1

    1. Find the "percent", the "is" and the "of". 2. Substitute the values into the proportion in the correct places and solve for the unknown value. 3. Check to make sure you have written your answer correctly. (%'s need a "%"!) This single method can solve every type of percent problem you will encounter!

  3. How to Solve Percent Problems? (+FREE Worksheet!)

    Solution: In this problem, we are looking for the percent. Use the following equation: \ (\color {blue} {Percent} = \color { black } {Part} \ ÷\) Base \ (→\) Percent \ (=2.5 \ ÷ \ 20=0.125=12.5\%\) The Absolute Best Books to Ace Pre-Algebra to Algebra II The Ultimate Algebra Bundle From Pre-Algebra to Algebra II Download $ 89.99 $ 49 .99

  4. Percentages Worksheets

    In the first few sections, there are worksheets involving the three main types of percentage problems: calculating the percentage value of a number, calculating the percentage rate of one number compared to another number, and calculating the original amount given the percentage value and the percentage rate.

  5. PDF Solve each problem. Round to the nearest tenth or tenth of a percent

    P i MMRa 3dxe S DwRilt ghE IqnDfLiAnGiut weR 1Azlugve DbUrga b z1H.a Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Percent Problems Date_____ Period____ Solve each problem. Round to the nearest tenth or tenth of a percent. 1) What percent of 29 is 3? 10.3%

  6. Percent Worksheets

    Converting Between Percents, Decimals & Fractions Percent Worksheets Detailed Description for All Percent Worksheets Table of Common Percents Percent Worksheets These percent worksheets are great for learning commonly recognized percents and their fraction and decimal equivalents.

  7. PDF Percent Equation P B A

    To solve the problem, identify the given and unknown parts: Given: Base = 120 Amount = 15 Unknown: Percent = x Equation: 120 • x = 15 120• x 120 15 = 120 x = 0.125 = 12.5% 0.125 120 15.000 Percent Proportion Problems involving the percent equation can also be solved with the proportion: Percent Amount (is) = 100 Base (of)

  8. Equations Worksheets

    Percentage Calculations Worksheets This Algebra 1 Worksheet is great for practicing percentage calculations. You may select three different types of problems and have the problems be in either numerical or word formats. You may select the range of numbers to work with as well as whole number or decimal numbers.

  9. 5.2.1: Solving Percent Problems

    To solve percent problems, you can use the equation, Percent ⋅ Base = Amount , and solve for the unknown numbers. Or, you can set up the proportion, Percent = amount base , where the percent is a ratio of a number to 100. You can then use cross multiplication to solve the proportion. Percents are a ratio of a number and 100, so they are ...

  10. Solving percent problems (video)

    25% is part of a whole 100%.*. *25% is 1/4 of 100%*. so, you know that (150) is 1/4 of the answer (100%) Add 150 - 4 times (Because we know that 25% X 4 = 100%) And that is equal to: (150 + 150 + 150 + 150) = *600. The method they used in the video is also correct, but i think that this one is easier, and will make it more simple to solve the ...

  11. IXL

    Recommendations. Skill plans. IXL plans. Virginia state standards. Textbooks. Test prep. Awards. Improve your math knowledge with free questions in "Solve percent equations" and thousands of other math skills.

  12. PDF Math 7 Name Chapter 6 Test

    Solve each problem using the equation method. Please show the equations and work for each problem in the space provided. 13. What number is 45% of 580? 13. _________________ 14. What percent of 160 is 62? 14. _________________ Solve each problem using the proportion method. Please show the proportion and work for each problem in the space provided.

  13. Percentage Equations Worksheets

    These sheets cover the most basic form of question to advanced and complex forms. Homework 1 - 4 is what % less than 80? Homework 2 - The equation that we use for percentage decrease is: difference of values/ larger value x 100%. Homework 3 - For all of the problems we need to determine the percentage decrease.

  14. Math: Basic Tutorials : Solving Percent Application Problems

    Solving Percent Application Problems Once you know the basics of how to solve operations with percent, you can use those methods to solve application problems. This section explains how to find the base, part, and percent in a word problem, and use them to solve the problem. Solving Percent Application Problems Solving Percent Application Problems

  15. Solving Percent Problems Using Equations Teaching Resources

    Browse solving percent problems using equations resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources.

  16. Percent Worksheets

    This ensemble of printable percentage worksheets is tailor-made for students of grade 6, grade 7, and grade 8. A plethora of exercises like finding the percent of the shaded region, finding percent of a whole numbers and decimals, comparing quantities, well-researched word problems and a lot more are available here.

  17. Using The Percent Equation Worksheets

    Using The Percent Equation - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Handouts on percents 2 percent word, Solving basic percent problems, Percent problems, Percent word problems, Percents, Name period date, Work math grade 7 introduction to percent, 6th math sample task scales.

  18. PDF Percent Problems: Proportion Method

    1 1 33 :100 or 33 to 100 3 3 A percent equation can be solved using proportions. You may wish to review proportions in your text. The proportion must have two equal ratios. One of the ratios will be determined by the Amount percent. The other ratio will be the Amount to the Base, written .

  19. Solving Percent Problems using Algebra (with videos, worksheets

    Videos, worksheets, and solutions to help Grade 8 students learn how to solve percent problems using Algebra. Learn how to solve percent problems algebraically. Algebra: Percent 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 ...

  20. Solving Percent Equations Worksheet

    Problem 1 : Solve for x : 20% of x is 16 Solution : 20% of x is 16 0.2x = 16 Divide each side by 0.2 x = 80 Problem 2 : Solve for x : x% of 18x is 0.9 Solution : x% of 18 is 0.9 0.01x ⋅ 18 = 0.9 0.18x = 0.9 Divide each side by 0.18 x = 5 Problem 3 : Solve for x : 15% of 50 is x

  21. The Percent Equation worksheet

    To solve percent problems using equation Liveworksheets transforms your traditional printable worksheets into self-correcting interactive exercises that the students can do online and send to the teacher.

  22. IXL

    Improve your math knowledge with free questions in "Solve percent equations" and thousands of other math skills.

  23. Percent Equation Teaching Resources

    This digital and Printable maze have three types of percent problems. Students will find the part, whole or percent. Percent equations practice is a great idea to review solving one-step equations. This product includes:Matching activity - Digital version on google slidesPrintable (color & black and white)Answer recording sheetsAnswer KeysWhy ...

  24. Solving Percent Problems With Equations Worksheets

    Solving Percent Problems With Equations - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Solve each round to the nearest tenth or tenth of, Percent word problems, Percents, Handouts on percents 2 percent word, Pre activity solving percent problems preparation, Solving proportions date period ...