# 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 conversion factors: $$\frac{400 \text{ euros}}{500 \text{ dollars}} \cdot \frac{1.3 \text{ dollars}}{1 \text{ euro}} = \frac{520}{500} = 1.04$$ which means the money is greater by $\boxed{ \textbf{(B)} \ 4 }$ percent.

## Solution 2

If we divide each of Etienne's and Diana's values by $100$, the problem stays the same. Then, Etienne has $1.3$ times the amount of money Diana has, so Etienne has $5.2$ dollars. Since $\dfrac{5.2}{5} = 1.04$, Etienne has $\boxed{ \textbf{(B)} \ 4 }$ percent more money than Diana. ~Extremelysupercooldude

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