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# Proportions to Find Part a

## Cross - multiply to find a missing part of a proportion, a.

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Proportions to Find Part a

Remember the candy percents? Well, there were also jelly beans in that bag. Look at it 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 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.

Once you know all of the other percents, you will know what percent of the bag are jelly beans. Given that percent, how many jelly beans are in the bag?

Let's look at the percents we discovered in the last Concept.

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.

Finally, we come to the jelly beans. Now we want to find out how many jelly beans are in the bag out of 40. What is the percent?

Well, we can find it if we think about the two other percents of candy in the bag. 25% is candy canes + 40% is peanut butter cups so 65% of the bag is filled leaving 35% for the jelly beans.

We can use this percent to use a proportion to figure out the number of jelly beans in the bag. Use this Concept to learn how to do this. It is the way we find part a of a proportion.

### Guidance

In the last Concept, we were given the amount and the base. The key words “of” let us know that we had a base and the other number naturally became the amount since we were looking for the percent.

Sometimes, you will be given the base and the percent and you will need to find the amount. You can use the same proportion to figure this out. You just need to fill in the numbers in the correct places and solve.

What is 25% of 75?

To figure this out, let’s look at what we have been given for information. First, we know the percent so we can fill in that half of the proportion.

$\frac{25}{100}$

We have been given the base. “Of 75” lets us know that this is the base. The amount is missing. That is our unknown.

$\frac{a}{75}$

Now let’s put it together as a proportion and use cross products to solve for $a$ .

$\frac{a}{75}& =\frac{25}{100}\\100a & = 25(75)\\100a & = 1875\\a & = 18.75$

Notice that we moved the decimal point two places to the left when we divided by 100.

Our answer is 18.75 or $18\frac{3}{4}$ .

Notice that there isn’t a percent sign here because we were looking for an amount not a percent!! This can trip up some students so always pay attention to what you are looking for!!!

Mr. Green bought both vegetable and flowering plants for his garden. He bought 40 plants and 35% were flowering plants. How many flowering plants did he buy?

We can think of this problem as “What is 35% of 40?”

40 is the base $(b)$ and 35 is the percent $(p)$ . We need to find the amount $(a)$ .

First, let’s set up the proportion.

$\frac{a}{40}=\frac{35}{100}$

Now we can use cross products to solve for the amount.

$100a & = 35(40)\\100a & = 1400\\a & = 14$

Mr. Green bought 14 flowering plants.

Now it's time for you to try a few.

#### Example A

What is 20% of 30?

Solution:6

#### Example B

What is 16% of 50?

Solution: 8

#### Example C

What is 22% of 80?

Solution: 17.6

Now back to the jelly beans. 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 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.

Once you know all of the other percents, you will know what percent of the bag are jelly beans. Given that percent, how many jelly beans are in the bag?

Let's look at the percents we discovered in the last Concept.

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.

Finally, we come to the jelly beans. Now we want to find out how many jelly beans are in the bag out of 40. What is the percent?

Well, we can find it if we think about the two other percents of candy in the bag. 25% is candy canes + 40% is peanut butter cups so 65% of the bag is filled leaving 35% for the jelly beans.

$\frac{a}{40} & = \frac{35}{100}\\100a & = 35(40)\\100a & = 1400\\a & = 14$

There are 14 jelly beans in the bag.

### 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 number is 15% of 60?

To figure this out, let's set up a proportion. Remember, the missing part is variable a.

$\frac{15}{100} = \frac{a}{60}$

Now we can cross multiply and solve.

$100a = 900$

$a = 9$

### Video Review

Here is a video for review.

### Practice

Directions: Find each missing amount.

1. What number is 25% of 18?

2. What number is 10% of 20?

3. What number is 45% of 16?

4. What number is 20% of 44?

5. What number is 30% of 100?

6. What number is 25% of 60?

7. What number is 40% of 80?

8. What number is 40% of 60?

9. What number is 50% of 120?

10. What number is 5% of 12?

11. What number is 5% of 20?

12. What number is 16% of 80?

13. What number is 25% of 23?

14. What number is 50% of 17?

15. What number is 30% of 33?

### Vocabulary Language: English

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.