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Percent Equation to Find Part a

Find x% of a number

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Percent Equation to Find Part a

Do you like jelly beans? Take a look at this dilemma.

Taylor’s younger brother Max decided to visit her at the candy store. Max is only seven and can be a handful sometimes, so while Taylor loves to see him, she was a little hesitant to have him in the shop. Plus, what seven year old doesn’t love candy.

Taylor gave Max a small bag to put some candy in. She figured he would take a few pieces, but ended up with a whole bunch of candy.

“How many did you take?” Taylor asked him looking in the bag.

“I took 40 pieces,” Max said grinning. “I won’t eat it all now. I will save some for later.”

Taylor looked into the bag. There were candy canes, peanut butter cups and a whole bunch of jelly beans.

She gave Max the bag and watched him walk away chewing.

“I hope I don’t get into trouble for this,” Taylor murmured to herself.

In looking in the bag, Taylor discovered that 15% of Max's bag was peanut butter cups. If he put 40 pieces of candy in his bag, how many pieces of candy were peanut butter cups?

We can say this another way using a percent equation.

What is 15% of 40?

This Concept will teach you how to use the percent equation to find part a. Then we will come back to this dilemma at the end of the Concept.

Guidance

Think about the proportion that you just learned to find the percent of a number.

\frac{a}{b}=\frac{p}{100}

When we used this proportion in problem solving, we multiplied b and p and a and 100. Then we divided the product of b and p by 100.

Let's look at a statement that uses this proportion.

What is 35% of 6?

First, we fill in the proportion.

\frac{a}{6}=\frac{35}{100}

Next, we multiply and solve for a .

100a & = 35(6)\\100a & = 210\\a & = 2.1

Notice that by dividing by 100, we moved the decimal place two places.

Hmmmm. This is the same two places that the percent is represented by. This means that if we changed the percent to a decimal FIRST, that we could skip a step and use an equation to find the missing value.

Take a look at the same problem.

What is 35% of 6?

First, change 35% to a decimal.

35\% = .35

Now we multiply it times 6, the base and find a the amount. Look at this equation.

a & = p\%(b)\\a & = .35(6) \\a & = 2.1

Notice that we got the same answer as when we used the proportion. It just simplifies the process.

Let’s look at another one.

What is 25% of 50?

First, change 25% to a decimal.

25\% = .25

Now use the equation.

a & = p\%(b)\\a & =.25(50)\\a & =12.5

The answer is 12.5.

Use the equation to find each amount. Include decimals in your answer.

Example A

What is 20% of 16?

Solution: 3.2

Example B

What is 5% of 40?

Solution: 2

Example C

What is 15% of 65?

Solution: 9.75

Here is the original problem once again.

Taylor’s younger brother Max decided to visit her at the candy store. Max is only seven and can be a handful sometimes, so while Taylor loves to see him, she was a little hesitant to have him in the shop. Plus, what seven year old doesn’t love candy.

Taylor gave Max a small bag to put some candy in. She figured he would take a few pieces, but ended up with a whole bunch of candy.

“How many did you take?” Taylor asked him looking in the bag.

“I took 40 pieces,” Max said grinning. “I won’t eat it all now. I will save some for later.”

Taylor looked into the bag. There were candy canes, peanut butter cups and a whole bunch of jelly beans.

She gave Max the bag and watched him walk away chewing.

“I hope I don’t get into trouble for this,” Taylor murmured to herself.

In looking in the bag, Taylor discovered that 15% of Max's bag was peanut butter cups. If he put 40 pieces of candy in his bag, how many pieces of candy were peanut butter cups?

We can say this another way using a percent equation.

What is 15% of 40?

To figure this out, we can convert 15% into a decimal.

15\% = .15

Next, we multiply .15 by 40.

40 \times .15 = 6

Six pieces of candy in the bag were peanut butter cups.

Guided Practice

Here is one for you to try on your own.

What is 32% of 200?

Answer

To figure this out, first we change the percent to a decimal.

32\% = .32

Next, we multiply this decimal by 200.

200 \times .32 = 64

32% of 200 is 64.

Video Review

Here is a video for review.

This is a James Sousa video on using the percent equation to find part a of a percent problem.

Explore More

Directions: Use the percent equation to find each amount.

1. What is 20% of 18?

2. What is 10% of 30?

3. What is 5% of 90?

4. What is 12% of 27?

5. What is 18% of 30?

6. What is 50% of 88?

7. What is 75% of 12?

8. What is 75% of 90?

9. What is 22% of 40?

10. What is 25% of 60?

11. What is 8% of 15?

12. What is 99% of 200?

13. What is 90% of 12?

14. What is 18.5% of 230?

15. What is 20.5% of 160?

Vocabulary

Amount

Amount

In a proportion, the amount is the part of the base that is being calculated.
Base

Base

In the context of the percent equation, the base is the part of the whole from which the amount is calculated.
Decimal

Decimal

In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of one-tenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).
Inverse Operation

Inverse Operation

Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.
Percent

Percent

Percent means out of 100. It is a quantity written with a % sign.
Proportion

Proportion

A proportion is an equation that shows two equivalent ratios.

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