ACT Math : Whole and Part
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Example Questions
Example Question #102 : Arithmetic
If n% of 400 is 260, then what is 20% of n?
13
31
15
14
25
13
n% of 400 is 260
A number as a percentage of a second number is equal to the first number divided by the second number, times 100%.
260 / 400 * 100% = .65 * 100% = 65%. n = 65.
20% of n?
20% of 65 is equal to 65 * 20 / 100 = 65 / 5 = 13.
Example Question #2 : How To Find The Part From The Whole With Percentage
Auditions are being held for the annual school musical. There are 18 roles available in the show. If 75 students try out, what percentage of the students will get a role in the musical?
28%
22%
26%
30%
24%
24%
Percentage is #roles / # students = 18 / 75 = 0.24 = 24%
Example Question #1 : Whole And Part
You are making cookies and mixing the dry ingredients: flour, white sugar and brown sugar. If the recipe calls for 3 1/4 cups of flour, 1/2 cup of white sugar and 3/4 cup of brown sugar, what percentage of the recipe is white sugar?
11.1%
20%
17.5%
10%
16.7%
11.1%
Total ingredients = 3 1/4 cups + 1/2 cup + 3/4 cup = 4 1/2 cups
White sugar percentage = white sugar / total = (1/2)/(9/2) = .111 = 11.1%
Example Question #1 : How To Find The Part From The Whole With Percentage
Jamie bought shoes for 30% off the regular price of $37.99, rounded to the nearest cent. If she wanted to use exact change to pay, how much would she need in coins?
Example Question #1 : How To Find The Part From The Whole With Percentage
A class has 25 students. If 60% of them are boys, how many students are girls?
12
10
18
15
10
If 60% of the students are boys, 40% are girls 
Example Question #1 : How To Find The Part From The Whole With Percentage
The preceding graph depicts students' favorite colors. If there are 30 students in the class, how many prefer blue?
7
9
8
6
6
20% of the students prefer blue. We can calculate the number of students that prefer blue by multiplying the percentage by the total number of students.
Example Question #1 : How To Find The Part From The Whole With Percentage
Round your answer to the nearest percentage.
To find how much percent 
Thus,
Example Question #1 : How To Find The Part From The Whole With Percentage
The Smith family consumed 35 pounds of table salt last year. As part of a healthier diet, they would like to cut their table salt consumption by 40% this year. In order to reach this goal, what is the maximum amount of salt, in pounds, that the Smith family can consume this year?
39
21
49
42
35
21
We need to first find 40 percent of the amount of table salt that the Smith family consumed in the previous year. In order to calculate this, we need to convert 40 percent into a decimal by moving the decimal place two spaces to the left and multiplying it by last year's salt consumption.
Now, we need to subtract this amount from last year's salt consumption in order to calculate this years reduced consumption for the Smith family.
Example Question #1 : How To Find The Whole From The Part With 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).
800 gallons
1000 gallons
960 gallons
160 gallons
960 gallons
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 #1 : Whole And Part
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?
500
285
80
350
500
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.
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