1995 AMC 8 Problem 8

Attempt Problem 8 of the 1995 AMC 8 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 1995 AMC 8 solutions, or check the answer key.

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

8.

An American traveling in Italy wishes to exchange American money (dollars) for Italian money (lire). If 30003000 lire =$1.60,= \$1.60, how many lire will the traveler receive in exchange for $1.00?\$1.00?
180180
480480
18001800
18751875
48754875
Answer: D
Concepts:ratio and proportion
Small hint:
Find how many lire equal one dollar using the given rate
Big hint:
$1.00\$1.00 is 1.001.60\dfrac{1.00}{1.60} of $1.60,\$1.60, so take that fraction of 30003000
Solution:
Since $1.00\$1.00 is 1.001.60=58\dfrac{1.00}{1.60} = \dfrac58 of $1.60,\$1.60, the traveler gets 58\dfrac58 of 30003000 lire.
That is 58×3000=1875\dfrac58 \times 3000 = 1875 lire.
Thus, the correct answer is D .
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