ACT Math : How to find the whole from the part with percentage

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #24 : Percentage

The average cow produces 8 gallons of milk per day. Scientists have found a vitamin supplement that can safely increase a cow’s milk production by 20%. If a dairy farm consisting of 100 cows uses the supplement, how many gallons of milk will the dairy farm now produce? (Assume each cow produces the average amount of milk per day).

Possible Answers:

1000 gallons

800 gallons

960 gallons

160 gallons

Correct answer:

960 gallons

Explanation:

First, determine the amount of milk cows will produce with the supplement: 8 + (.2 x 8)= 9.6 gallons per day. Next, determine the amount of milk 100 cows will produce when receiving the supplement: 100 x 9.6 = 960 gallons.

 

 

Example Question #25 : Percentage

Florida Clementines Corp sells only the best clementines. The inspector rejected 50% of January’s harvest. Unfortunately, 20% of the inspected clementines fell off the delivery truck. If the truck delivers 200 clementines, how many were harvested in January?

 

Possible Answers:

80

350

500

285

Correct answer:

500

Explanation:

We first obtain how many clementines were loaded on the delivery truck from 200 delivered clementines. Then we obtain how many clementines were inspected. 200 = (1-0.2)x gives us 250 loaded onto the delivery truck. 250 = (1-0.5)x gives us 500 harvested clementines.

 

 

Example Question #1 : How To Find The Whole From The Part With Percentage

Ed eats 3 cookies every day. If he increases the total amount of cookies he has to begin with by 50%, it would take 21 days to finish all of his cookies. How many cookies does he have to begin with?

Possible Answers:

21 cookies

12 cookies

42 cookies

63 cookies

Correct answer:

42 cookies

Explanation:

We let T be the total amount of cookies and D be the number of days it takes to eat all of the cookies before increasing by 50%, and A be the number of days after increasing by 50%. With the information given, we can write the expressions, T=3D and 1.5T=3A. For the second equation, we know A=21. We plug in and get T=42.

Example Question #27 : Percentage

There are 8 blue balls in a bag. 40% of all the balls in the bag are blue. How many total balls are in the bag?

Possible Answers:

8

20

12

4

2

Correct answer:

20

Explanation:

You evaluate 8/0.4 = 20.

Example Question #28 : Percentage

95 is 20% of what number?

Possible Answers:

550

500

400

475

Correct answer:

475

Explanation:

multiply the part times 100 then divide by the percent. 

(95 x 100) / 20 = 475

Example Question #2 : How To Find The Whole From The Part With Percentage

If \dpi{100} \small 80\% of a number is \dpi{100} \small 240, what is \dpi{100} \small 125\% of the number? 

Possible Answers:

\dpi{100} \small 375

\dpi{100} \small 250

\dpi{100} \small 300

\dpi{100} \small 200

\dpi{100} \small 325

Correct answer:

\dpi{100} \small 375

Explanation:

Since \dpi{100} \small 80\% of the number is \dpi{100} \small 240, the number is \dpi{100} \small \frac{240}{.80} which equals \dpi{100} \small 300. Then calculate \dpi{100} \small 125\% of \dpi{100} \small 300:

\dpi{100} \small 1.25\times 300=375

Example Question #30 : Percentage

Gwen has a collection of 1,000 books.  The average thickness of each book is 1.25” thick.  She wants to buy enough bookshelves that all of her books will fit on it. 

What is the shortest length of bookshelf she should buy, in whole feet, to fit all her books?

Possible Answers:

105 feet

115 feet

120 feet

110 feet

125 feet

Correct answer:

105 feet

Explanation:

Length of books = 1,000 books x 1.25” per book = 1,250”

Translate to feet

1” = 12’

1250” / 12 = 104.16 feet

Round up to 105 feet to be able to fit all the books.

Example Question #3 : How To Find The Whole From The Part With Percentage

Nathan spends  of his total homework time on Math. He spends one hour on Biology homework, which is twice the amount of time that he spends on Math. What is the total amount of time, in minutes, that Nathan spends on homework?

Possible Answers:

Correct answer:

Explanation:

If  minutes of Biology () is twice as much time as that which is spent on Math (), then Math must equal 30 minutes.

, so .

 minutes is equivalent to  of the total time ():

Solve for by dividing both sides of the equation by .

Example Question #4 : How To Find The Whole From The Part With Percentage

A bowl contains  marbles that are either red or green. The probability of selecting a red marble at random from the bowl is 

Which of the following expressions represents the total number of red marbles in the bowl?

 

Possible Answers:

Correct answer:

Explanation:

It’s best to start with a fraction that is a part over 100. For this problem, we are looking for a fraction that shows .  If you go through the choices available, . Therefore, if you plug in any value for “X” in this fraction, you will know the total number of marbles in the bowl. Here is an example:

If there are 4 marbles in the bowl, you’d expect 1 to be red. If we use this equation, we get

 

 

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