Question

Of the $500$ balls in a large bag, $80\%$ are red and the rest are blue. How many of the red balls must be removed so that $75\%$ of the remaining balls are red?

$\ 25$

$\ 50$

$\ 75$

$\ 100$

$\ 150$

Answer: D

Concepts:percentage

Difficulty rating: 1120

Solution:

If $r$ is the number of red balls, then $r = 0.8\cdot500 = 400.$ Therefore, if $b$ is the number of blue balls, then $b = 500-400 = 100.$

If there are $75\%$ red balls after removing balls, then there are $25\%$ blue balls. This means the total number of balls is $\dfrac{100}{.25} = 400.$ This means the total number of balls decreased by $500-400 = 100.$

Thus, the answer is D .

2010 AMC 8 Problem 12

Answer: D

Difficulty rating: 1120

Solution:

Problem 12 in Other Years