2010 AMC 8 Problems/Problem 15

Problem

A jar contains $5$ different colors of gumdrops. $30%$ (Error compiling LaTeX. Unknown error_msg) are blue, $20%$ (Error compiling LaTeX. Unknown error_msg) are brown, $15%$ (Error compiling LaTeX. Unknown error_msg) are red, $10%$ (Error compiling LaTeX. Unknown error_msg) are yellow, and other $30$ gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how gumdrops will be brown?

$\textbf{(A)}\ 35\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 64$

Solution

We do $100-30-20-15-10$ to find the percent of gumdrops that are green. We find that $25%$ (Error compiling LaTeX. Unknown error_msg) of the gumdrops are green. That means there are $120$ gumdrops. If we replace all blue gumdrops with green gumdrops, then $35%$ (Error compiling LaTeX. Unknown error_msg) of the jar's gumdrops are brown. $\dfrac{35}{100} \cdot 120=42 \Rightarrow \boxed{\textbf{(C)}\ 42}$

2011 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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2010 AMC 8 Problems/Problem 15

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