Art of Problem Solving
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2010 AMC 8 Problems/Problem 15: Difference between revisions

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==Problem==
==Problem==
A jar contains <math>5</math> different colors of gumdrops. <math>30%</math> are blue, <math>20%</math> are brown, <math>15%</math> are red, <math>10%</math> are yellow, and other <math>30</math> gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how gumdrops will be brown?
A jar contains <math>5</math> different colors of gumdrops. <math>30%</math> are blue, <math>20%</math> are brown, <math>15%</math> are red, <math>10%</math> are yellow, and other <math>30</math> gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how gumdrops will be brown?
<math> \textbf{(A)}\ 35\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 64 </math>
<math> \textbf{(A)}\ 35\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 64 </math>



Revision as of 16:31, 5 November 2012

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. $\dfrac{35}{100} \cdot 120=42 \Rightarrow \boxed{\textbf{(C)}\ 42}$

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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All AJHSME/AMC 8 Problems and Solutions