Problem 14 · 1992 AJHSME
Medium
Fractions, Decimals & Percents
fraction-of
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
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Answer: D — 24.
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Hint 1 of 3
The 4 gallons didn't fill the tank — they just nudged the level from 1/3 up to 1/2. What single fraction of the tank does that little rise represent?
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Hint 2 of 3
Once you know what fraction a known amount fills, scale up: if a fraction is some gallons, the whole is that many gallons × (how many of that fraction fit in a whole).
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Hint 3 of 3
Subtract the two level-fractions using a common denominator to find the rise.
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Approach: find the fraction the 4 gallons fills, then scale up to the whole
- The level rose from 1/3 to 1/2. The rise is 1/2 − 1/3 = 3/6 − 2/6 = 1/6 of the tank. So 1/6 of the tank = 4 gallons.
- A whole tank is 6 such sixths, so capacity = 6 × 4 = 24 gallons.
- Why this transfers: "x units fill a fraction — find the whole" is always the same move: figure out what fraction the known amount represents, then multiply by however many of those fractions make one whole.
- Sanity check: 1/3 of 24 = 8 gallons; add 4 to get 12, which is exactly 1/2 of 24. The story holds together.
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