Now that you can find the value of a percent, you can turn our attention to problems that use a percent to find another value. If you know the size of the whole group and you know what percent you are looking for, how can you find the size of the smaller group?

A percent bar can still help you with a problem like this. The difference is that you know the percent and want to know the part of the whole. In section 1, we carefully measured and marked the bar in 10% increments; in this section, we will break the bar into even divisions of the whole so that we can better tell the value of the part.

Look at the following example problem:

Mr. Martinez is giving a 60 question final exam in his social studies classroom. Steve figures that he needs to get 75% of the questions correct in order to pass the semester. Use that equation to check your answer for the number of questions that Steve needs to get correct.

What is the total number of questions on the test?

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What are reasonable divisions for the left side of the percent bar?

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Mark the bar from 0 to 60 questions with divisions for every 5 questions.
empty percent bar with a scale marked from 0 to 60 in intervals of 5

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How many questions does Steve need to get correct in order to pass?

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Steve needs to get 45 questions correct in order to pass.

Now, let's use the percent bar and a scale factor.

percent bar filled to show that 15 is 25% of 60

Using this percent bar, what is 25% of 60?

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25% of 60 is 15.

What factor do you use to move from 25% to 75%?

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A factor of 3.

Use this factor to determine the number of questions Steve needs to get correct.

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15(3) = 45
Steve needs to get 45 questions correct in order to pass.

Recall the proportional relationship that we set up in section 1:

part over whole part whole = percent over 100 percent 100

What is the general form of the equation that represents a proportional relationship? (See lesson 7 in module 1 if you need a review)

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y = kx

Given that:

y → part
x → whole
k → percent over 100 percent 100

Rewrite the equation using the terms, part, whole and percent over 100 percent 100.

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part = percent over 100 percent 100 * whole

Use the equation from the previous question to check your answer and to solve for the number of questions that Steve needs to get correct.

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Part = 75 over 100 75 100 (60)
Part = 0.75(60)
Part = 45
Steve needs to get 45 questions correct in order to pass.

Solve each of the following examples by sketching your own percent bar or by using a calculator. If you need a hint, click on the hint button:

(Hints and solutions are shown for all three methods that we have covered, but you only need to use one method to find your own solution.)

A recent report from the U.S. department of energy listed the oil imports for July of 2011. In July 2011, the United States purchased an average of about 9 million barrels of oil from other countries every day. The greatest number of barrels of oil purchased was from Canada. If the oil purchased from Canada represents 24% of the total purchased, how many barrels of oil did we buy from Canada each day?

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Hint

Percent Bar Estimate
percent bar filled to 24% out of 100. Unknown part marked between 2 and 3

Calculator
part = percent over 100 percent 100 * whole
part = 24 over 10 24 100 * 9
part = 0.24 * 9

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Part = 2.16
The United States bought about 2.16 million barrels of oil from Canada every day in July.

A store is holding a clearance sale with everything to be sold at 25% off the regular price. If the original price of an item is $20.00, how much will you save?

Hints:

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Percent Bar Estimate

percent bar filled to 25% out of 100. Unknown part marked between 4 and 6

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Percent Bar Scale

percent bar filled to show that 2 is 10% of 20

10% of 20 is 2
The factor to move from
10% → 25% is 2.5

25% of 20 is 2(2.5)

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Calculator

part = percent over 100 percent 100 * whole
part = 25 over 100 25 100 * 20
part = 0.25 * 20

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Part = 5
You will save $5.00

Sales Tax:

When you buy something at a store, the total that you pay is always a little bit higher than what the item costs. You also pay a percent of the price as sales tax. Depending on where you live in Texas, the sales tax can be up to 8.25%.

Your parents decide to paint the living room. When they go to the paint store, they find that they need to buy $75.00 worth of paint. If the sales tax rate is 8%, how much money will be added to the price of the paint?

Hints:

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Percent Bar Estimate

percent bar filled to 8% out of 100. Unknown part marked between 5 and 10

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Percent Bar Scale

percent bar filled to show that 7.5 is 10% of 75 and 15 is 20% of 75

20% of 75 is 15
The factor to move
20% → 8% is 2 over 5 2 5
8% of 75 is 2 over 5 2 5 (15)

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Calculator

part = percent over 100 percent 100 * whole
part = 8 over 100 8 100 * 75
part = 0.08 * 75

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Check Your Answer

Part = 6
There will be $6.00 in tax added to the total.