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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
8.6 Percentage Problems

Formula:
percent x whole = part
or
percent = part/whole
or
%/100 = part/whole


Percentage Problems:
For percentage word problems replace "what is" to "n", "is to" to "=" and "of" to "x"
A is B% of what number? (A and B are unknown)
A = B% x n
n = A / B%
A is what percent of B?
A = n% x B
n =(A/B) x 100
What percent of A is B?
n% x A = B
n = (B/A) x 100
What is A% of B?
n = A% x B

What is the percentage change when A becomes B?
!A - B)/A x 100 = n

Example:
12 is 50% of what number?
Solution:
Let 'n' be the unknown number.
12 is 50 % of what number
12 = 0.5 x n
So, the equation to solve then is: 0.5 x n =12
Solving for n, we get n = 12/0.5 = 24
This means, 12 is 50 % of 24

Example:
40 is what percent of 160?
Solution:
Let 'n' be the unknown percent.
40 is what percent of 160?
40 = n x 160
So, the equation to solve then is: 160 x n =40
Solving for n, we get n=40 /160
n=0.25
To make 0.25 into a percent, we multiply it by 100, to get 25 %.
This means 40 is 25 % of 160

Example:
What percent of 80 is 20?
Solution:
Let 'n' be the unknown percent.
What percent of 80 is 20?
n x 80 = 20
So, the equation to solve then is: 80 x n=20
Solving for n, we get n=20 /80
n=0.25
This means, 20 is 25 % of 80

Example:
What is 15% of 200?
Solution:
Convert 15% to number as 15/100 = 0.15
15% of 200
=0.15 x 200
= 30

Example:
What percentage difference is the number 12 from the number 16?
Solution:
The difference is 16 - 12 = 4
The percentage difference = (4/16) x 100
25%

Directions: Solve the following word problems.
Q 1: What percent of 400 is 20?
5%
15%
10%

Q 2: 17 is 25% of what number?
70
68
56

Q 3: What is 17% of 400?
79
68
56

Q 4: What is the percentage change when 310 becomes 620?
50%
100%
25%

Q 5: What percent of 98 is 49?
75%
50%
35%

Q 6: What is the percentage change when 306 becomes 153?
45%
60%
50%

Q 7: 40 is 20% of what number?
200
300
250

Q 8: 45 is what percent of 180?
50%
25%
20%

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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