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6.5: Proportions to Find Percent, P

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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 10 candy canes, 16 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.

Think about the candy in Max’s bag. It makes for some great math problems. If there are 40 pieces of candy, what percent of Max’s bag is made up of candy canes? What percent of his bag is made up of peanut butter cups?

Use this Concept to learn all about calculating percents.

Guidance

First, let’s review what a percent is.

A percent is a part of a whole out of 100 .

We can write a percent as a fraction with a denominator of 100.

We can use a proportion to figure out a percent.

Look at this proportion, $\frac{a}{b}=\frac{p}{100}$ .

We can say that “ $a$ is the amount to the base, $b$ , and $p$ is the percent out of 100.”

That may sound a little tricky, but if you get used to thinking in this way, you will find that this is very helpful when solving for one of the missing parts of the proportion. Since percent statements always involve three numbers, given any two of these numbers, we can find the third number using the proportion.

What percent of 40 is 6?

First, thing to notice is that we are looking for the percent. So the $p$ over 100 is going to stay the same in the proportion.

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

We need to fill in the $a$ and the $b$ so we can solve for $p$ , the percent. The words “of 40” lets us know that 40 is the base and 6 is the amount.

Here is our proportion to solve.

$\frac{6}{40}=\frac{p}{100}$

Now we can use cross products and solve.

$40p & = 600\\p & = 15$

Jeremy has 25 marbles and 12 of them are cat’s eye marbles. What percent of his marbles are cat’s eye marbles?

We can think of this problem as “What percent of 25 is 12?”

12 is the amount $(a)$ and 25 is the base $(b)$ . We need to find the percent $(p)$ .

$\frac{a}{b}& =\frac{p}{100}\\\frac{12}{25}& =\frac{p}{100}\\25p& =1,200\\\frac{25p}{25}& =\frac{1,200}{25}\\p& =48$

Since $p = 48, \frac{48}{100}$ , which is 48%.

The answer is that 48% of Jeremy’s marbles are cat’s eye marbles.

Use a proportion to find each percent.

Example A

What percent of 20 is 2?

Solution: $10\%$

Example B

What percent of 30 is 6?

Solution: $20\%$

Example C

What percent of 45 is 15?

Solution: $33.3\%$

Here is the original problem once again. Reread it and use what you have learned about percents to figure out the questions at the end of the problem.

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 10 candy canes, 16 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.

Think about the candy in Max’s bag. It makes for some great math problems. If there are 40 pieces of candy, what percent of Max’s bag is made up of candy canes? What percent of his bag is made up of peanut butter cups?

First, let’s figure out the percents.

We start with candy canes. There are 10 out of 40. There is our first ratio, and now we need to find the percent.

$\frac{10}{40}& =\frac{p}{100}\\p & = 25\%$

25% of the bag is candy canes.

Next, let’s look at the peanut butter cups. 16 out of 40 are peanut butter cups.

$\frac{16}{40}& =\frac{p}{100}\\40p & = 1600\\p & = 40\%$

40% of the bag is peanut butter cups.

Vocabulary

Here are the vocabulary words in this Concept.

Percent
a part of a whole out of 100
Proportion
formed by two equal ratios or two equivalent fractions

Guided Practice

Here is one for you to try on your own.

What percent of 300 is 40?

To figure this out, we can use the following percent proportion.

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

Now we can fill in the given information.

$\frac{40}{300} = \frac{p}{100}$

Now we can cross multiply and divide.

$300p = 4000$

$p = 13.3\%$

Video Review

Here is a video for review.

Practice

Directions: Find each percent using a proportion.

1. What percent of 18 is 9?

2. What percent of 20 is 4?

3. What percent of 28 is 7?

4. What percent of 30 is 6?

5. What percent of 9 is 3?

6. What percent of 36 is 18?

7. What percent of 40 is 8?

8. What percent of 48 is 12?

9. What percent of 50 is 30?

10. What percent of 80 is 60?

11. What percent of 90 is 12?

12. What percent of 75 is 25?

13. What percent of 60 is 12?

14. What percent of 50 is 40?

15. What percent of 88 is 11?

Basic

Date Created:

Nov 30, 2012

Aug 08, 2014
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