1992 AMC 8 Problem 14

Attempt Problem 14 of the 1992 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 1992 AMC 8 solutions, or check the answer key.

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

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
Answer: D
Concepts:fractionlinear equation
Small hint:
Adding 44 gallons raises the tank from 13\dfrac13 full to 12\dfrac12 full
Big hint:
So 44 gallons equals 12−13=16\dfrac12 - \dfrac13 = \dfrac16 of the capacity
Solution:
The 44 gallons account for the change from 13\dfrac13 full to 12\dfrac12 full, which is 12−13=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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