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Difference between revisions of "2014 AMC 12B Problems/Problem 4"

(Created page with "==Problem== Susie pays for <math> 4 </math> muffins and <math> 3 </math> bananas. Calvin spends twice as much paying for <math> 2 </math> muffins and <math> 16 </math> bananas. ...")
 
(→‎Solution)
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<cmath>\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}</cmath>
 
<cmath>\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}</cmath>
  
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Solution by kevin38017
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(Solution by kevin38017)

Revision as of 16:25, 20 February 2014

Problem

Susie pays for $4$ muffins and $3$ bananas. Calvin spends twice as much paying for $2$ muffins and $16$ bananas. A muffin is how many times as expensive as a banana?

$\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{7}{4}\qquad\textbf{(D)}}\ 2\qquad\textbf{(E)}\ \frac{13}{4}$ (Error compiling LaTeX. Unknown error_msg)

Solution

Let $m$ stand for the cost of a muffin, and let $b$ stand for the value of a banana. We we need to find $\frac{m}{b}$, the ratio of the price of the muffins to that of the bananas. We have \[2(4m + 3b) = 2m + 16b\] \[6m = 10b\] \[\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}\]

(Solution by kevin38017)

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