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### Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation8.6 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 is the percentage change when 306 becomes 153?45%50%60% Q 2: What percent of 98 is 49?50%35%75% Q 3: What is the percentage change when 310 becomes 620?25%100%50% Q 4: What percent of 400 is 20?10%5%15% Q 5: 40 is 20% of what number?200250300 Q 6: What is 20% of 2000?400500200 Q 7: 45 is what percent of 180?25%20%50% Q 8: What is 17% of 400?795668 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!