Proportions to Find Part a
Jen Kershaw
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Printed: October 21, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Proportions to Find Part a
1
Proportions to Find Part a
Here you’ll learn to use a proportion 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.
10
p
=
40 100
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.
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p
16
=
40 100
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.
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.
a
75
Now let’s put it together as a proportion and use cross products to solve for a.
a
25
=
75 100
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 43 .
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Chapter 1. Proportions to Find Part a
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.
a
40
=
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.
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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.
4
www.ck12.org
Chapter 1. Proportions to Find Part a
p
10
=
40 100
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.
16
p
=
40 100
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.
35
a
=
40 100
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?
Answer
To figure this out, let’s set up a proportion. Remember, the missing part is variable a.
15
100
=
a
60
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Now we can cross multiply and solve.
100a = 900
a=9
This is our answer.
Video Review
Here is a video for review.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5510
This James Sousa video is about solving a percent problem by using a proportion.
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?
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