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

## Video Solution 1 (Quick and Easy)

~Education, the Study of Everything

## See also

 2014 AMC 12B (Problems • Answer Key • Resources) Preceded byProblem 3 Followed byProblem 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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
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