2012 AMC 12B Problem 4

Attempt Problem 4 of the 2012 AMC 12B below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Suppose that the euro is worth 1.301.30 dollars. If Diana has 500500 dollars and Étienne has 400400 euros, by what percent is the value of Étienne’s money greater than the value of Diana’s money?
22
44
6.56.5
88
1313
Answer: B
Concepts:percentageunit conversion
Small hint:
Convert Étienne’s euros to dollars first
Big hint:
The percent increase is Eˊtienne−DianaDiana⋅100%\dfrac{\text{Étienne} - \text{Diana}}{\text{Diana}}\cdot100\%
Solution:
Étienne’s money is worth 400⋅1.30=520400\cdot1.30=520 dollars, while Diana has 500500 dollars.
The percent by which Étienne’s value exceeds Diana’s is 520−500500⋅100%=4%.\frac{520-500}{500}\cdot100\%=4\%.
Thus, the correct answer is B.
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