1992 AMC 8 Problem 14

Below is the professionally curated solution for Problem 14 of the 1992 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1992 AMC 8 solutions, or check the answer key.

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Concepts:fractionlinear equation

Difficulty rating: 930

14.

When four gallons are added to a tank that is one-third full, the tank is then one-half full. The capacity of the tank in gallons is

88

1212

2020

2424

4848

Solution:

The 44 gallons account for the change from 13\dfrac13 full to 12\dfrac12 full, which is 1213=16\dfrac12 - \dfrac13 = \dfrac16 of the capacity.

If 16\dfrac16 of the capacity is 44 gallons, the full capacity is 4×6=244 \times 6 = 24 gallons.

Thus, the correct answer is D .

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