Question

A jar contains $5$ different colors of gum drops. $30\%$ are blue, $20\%$ are brown, $15\%$ are red, $10\%$ are yellow, and the other $30$ gum drops are green. If half of the blue gum drops are replaced by brown gum drops, how many gum drops will be brown?

$\ 35$

$\ 36$

$\ 42$

$\ 48$

$\ 64$

Solution:

Since we have percentages for every color except green, the percent of green is $100\%$ minus the sum of the other colors. This would make the percent of green equal to $100\%-30\%-20\%-$ $15\%-10\% = 25\%$

Since we know $30$ gum drops is $25\%,$ we know that the total number of gum drops is $\dfrac { 30}{.25} = 120.$

This means there are $.2*120 = 24$ brown gum drops to start and $.3*120 = 36$ blue gum drops. If half of the blue gum drops are turned to brown, then $\dfrac{36}{2} = 18$ more brown gum drops are added. Therefore, we have $24+18= 42$ brown gum drops.

Thus, the answer is C .

2010 AMC 8 Problem 15

Solution:

Problem 15 in Other Years