Percent Word Problems

In this lesson, we will be working with percents. If you have worked with fractions and know what a percent is, you already have a good base for this lesson. Think about percents and what they mean as a fraction. What does 25% mean? If you remember it means 25 out of 100 or 25/100.

QUESTION: Can it be said that is a ratio or that percents can be written as ratios?

ANSWER: YES!!!! Percents can always be written as a ratio between a number and 100.

Since percents can be written as ratios, we can say that percent problems can also be worked using proportions.

All percent problems fit the proportion:

equation image indicator $LaTeX: \frac{is}{of}=\frac{\%}{100}$

One could say that 40% of 60 is 24. Placing these numbers into the proportion gives us

$LaTeX: \frac{24}{60}=\frac{40}{100}$

Remember, percent means out of 100, so the denominator of the percent ratio will always be 100. If one of the parts of the proportion is missing, we use a letter to represent the unknown. Then we can use the cross-product to find our unknown portion.

Let's take a look at a problem where we need to find some information. We use percents in our everyday life such as a sale on clothes at department stores, the percent of games won, and surveys.

Example 1

At the department store, we find a pair of shoes on sale. We want to make sure we have enough money to buy them. According to the sign, the price of the shoes is 80% of the full price of $56. What is the sale price?

Step 1:

Set up of the proportion:

$LaTeX: \frac{x}{56}=\frac{80}{100}$

Step 2:

Use the cross-product property to solve for x!!

100x = 4480

x = 44.8

"A percent of a number is another number." This phrase can be used to solve percent word problems. The word "of" in math means to multiply. The word "is" in math means equal. So you should multiply the percent (written as a decimal) times the given number. The answer is the product.

Example 2

Sales tax is 5% in Maryland. Jim bought a pair of basketball shoes advertised for $62. How much sales tax did he pay?

Step 1:

Convert your percent to a decimal.

5% = 0.05 (move the decimal two places to the left)

Step 2:

Multiply the decimal by the price.

0.05 times $62 equals the Maryland sales tax

0.05 (62) = ?

The sales tax was $3.10 in Maryland.

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