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

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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. A muffin is how many times as expensive as a banana?
 
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. A muffin is how many times as expensive as a banana?
  
<math> \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} </math>
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<cmath> \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} </cmath>
  
 
==Solution==
 
==Solution==

Revision as of 13:33, 24 January 2015

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 \[2(4m + 3b) = 2m + 16b\] \[6m = 10b\] \[\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}\]

See also

2014 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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