Percent Word Problems
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Introduction

    This lesson will inform you how to solve percent word problems or problems that contain percents. Here are the sections within this page:

    To fully understand the sections that follow, it is crucial that you understand how to solve equations and how to work with ratios (otherwise known as fractions). Use these lessons if you need to prepare yourself.

    esson: Fractions
    esson: Solving Equations


    Percents are used in a variety of capacities. Here are some common areas:

Common Areas Where Percents are Found
NutritionDetermining daily content for calorie, sodium, and fat intake.
ShoppingFinding sale price, tax, or tip amount (restaurants).
SalesCalculating the amount of money made from commission.
ValueAdjusting the value for an item, either appreciation or depreciation



    This is an important question to consider: "What is a percent?" Let us examine the word 'percent.' The word literally means per 100 because cent means 100. So, a percent is a ratio.

    For instance, 50% means 50 per 100. But, 50/100 is the same as 1/2. Therefore, 50% is equivalent to a half.

    To gain a visual on what 50% looks like, the glass below is at 50% or 1/2 capacity.

    Likewise, 75% means 75/100, which reduces to 3/4. So 75% = 3/4.

    Now that you have an idea of what percents mean, we need to look at the word problem portion of percent word problems.


    There are certain words that translate to mathematics. This may not always be true, but is almost always true. Examine the table below to see the conversion between words and mathematics.

Conversion: Words to Mathematics
whatx
is=
ofmultiply
percentover 100

    When we see either the words 'what,' 'is,' 'of,' or 'percent,' we will substitute their mathematical meaning into an equation. Then, we will solve the equation. Use the three types of problems below to see how it is done.


    A type 1 problem could look like this.

"What number is 15% of 60?"

To solve this problem, we need to convert the problem from words into mathematics. Here is a word to mathematics translation.

To solve the resulting equation, we progress as follows.

    Now, we need to reduce the resulting fraction (or simplify with a calculator).

    So, 9 is 15% of 60.

    ideo: Percent Word Problems
    uiz: Percent Word Problems


    Here is a second type of word problem.

"20 is 30% of what number?"

    Again, we need to convert this problem into mathematics. Here is the translation.

    Now, we will solve this equation.

    To solve this equation, we have to multiply the coefficient of the x-term by its reciprocal. This means both sides have to be multiplied by this quantity, like so.

    Now, we need to reduce the fraction (or use a calculator) to get our final answer.

    So, 20 is roughly 30% of 66.7.

    ideo: Percent Word Problems
    uiz: Percent Word Problems


    Here is the last type of word problem.

"40 is what percent of 500?"

    This sentence needs to be converted into mathematics, like so.

    Now, we will solve the resulting equation.

    To further solve this equation, we need to divide both sides by 5.

    So, 40 is 8% of 500.

    ideo: Percent Word Problems
    uiz: Percent Word Problems


    Try this instructional video to gain a more personalized view on this topic.

    ideo: Percent Word Problems


    Try this interactive quiz to test your knowledge of percent word problems.

    uiz: Percent Word Problems