2012 AMC 12B Problems/Problem 4

Problem

Suppose that the euro is worth 1.3 dollars. If Diana has 500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater that the value of Diana's money?

$\textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6.5\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 13$

Solution

The ratio $\frac{400 \text{ euros}}{500 \text{ dollars}}$ can be simplified using simple dimensional analysis:

$\frac{400 \text{ euros}}{500 \text{ dollars}} \cdot \frac{1.3 \text{ dollars}}{1 \text{ euro}} = \frac{520}{500} = 1.04$ , which means a value that is greater by $\boxed{ \textbf{(B)} \ 4 }$ percent.

2012 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2012 AMC 12B Problems/Problem 4

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