2012 AMC 12B Problem 4

Below is the professionally curated solution for Problem 4 of the 2012 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12B solutions, or check the answer key.

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Concepts:percentage unit conversion

Difficulty rating: 1050

Suppose that the euro is worth $1.30$ dollars. If Diana has $500$ dollars and Étienne has $400$ euros, by what percent is the value of Étienne's money greater than the value of Diana's money?

$2$

$4$

$6.5$

$8$

$13$

Solution:

Étienne's money is worth $400\cdot1.30=520$ dollars, while Diana has $500$ dollars.

The percent by which Étienne's value exceeds Diana's is $\frac{520-500}{500}\cdot100\%=4\%.$

Thus, the correct answer is B.

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