2014 AMC 12B Problems/Problem 4

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?

$\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{7}{4}\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{13}{4}$

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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