1953 AMC 12 Problem 9

Attempt Problem 9 of the 1953 AMC 12 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 1953 AMC 12 solutions, or check the answer key.

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

The number of ounces of water needed to reduce

9

ounces of shaving lotion containing

50\%

alcohol to a lotion containing

30\%

alcohol is:

3

4

5

6

7

The amount of alcohol stays fixed when water is added

Set

\frac{4.5}{9+w}=0.30

The lotion initially contains

9(0.50)=4.5

ounces of alcohol. If

w

ounces of water are added, then

\frac{4.5}{9+w}=0.30.

Hence

9+w=15

and

w=6.

Thus, the correct answer is D.

Problem 9 in other years