Problem:
Suppose 15% of x equals 20% of y. What percentage of x is y?
Answer Choices:
A. 5
B. 35
C. 75
D. 13331
E. 300
Solution:
First note that 15%=0.15, and 20%=0.2 It is given that 15% of x equals 20% of y, so
0.15x=0.20y
Solving for y yields
y=0.200.15x=2015x=10075x.
Therefore y is 75% of x.
OR
Let x=100 Then 15% of x is 15. This equals 20% of y, which is the same as 51y Solving the equation 15=51y yields y=5⋅15=75. Therefore y is 75% of x.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions