Problem 21 · 1991 AJHSME
Medium
Algebra & Patterns
linear-rate
For every 3° rise in temperature, the volume of a certain gas expands by 4 cubic centimeters. If the volume of the gas is 24 cubic centimeters when the temperature is 32°, what was the volume in cubic centimeters when the temperature was 20°?
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Answer: A — 8.
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Hint 1 of 3
The rule comes in chunks of 3° at a time, so think in STEPS, not in single degrees. Going from 32° back to 20° is how big a temperature change — and how many whole 3° steps does that make?
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Hint 2 of 3
Lower temperature means a SMALLER volume (the gas was colder before), so you'll subtract. A 12° drop = four 3° steps, and each step is worth 4 cm³.
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Hint 3 of 3
Find the change first (four steps × 4 cm³), then apply it to the known 24 cm³ in the right direction.
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Approach: count whole 3° steps, then subtract (colder = less)
- The rule changes volume only per 3° step, so measure the temperature change in steps. From 32° down to 20° is a 12° drop = 12 ÷ 3 = four steps.
- Each step is 4 cm³, so four steps = 16 cm³. Since we're going to a colder 20°, the gas was smaller then — subtract: 24 − 16 = 8 cm³.
- Trap to dodge: the easy slip is adding (getting 40) — always check direction: lower temperature shrinks the gas, so the earlier, cooler volume must be the smaller one.
- Why this transfers: for any "so much change per fixed step" rule, count the steps first, multiply by the per-step amount, then add or subtract based on which way you're traveling.
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