1991 AMC 8 Problem 21

Attempt Problem 21 of the 1991 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 1991 AMC 8 solutions, or check the answer key.

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

21.

For every 3∘3^\circ rise in temperature, the volume of a certain gas expands by 44 cubic centimeters. If the volume of the gas is 2424 cubic centimeters when the temperature is 32∘,32^\circ, what was the volume of the gas in cubic centimeters when the temperature was 20∘?20^\circ?
88
1212
1515
1616
4040
Answer: A
Concepts:ratework backwards
Small hint:
The temperature dropped from 32∘32^\circ to 20∘,20^\circ, a change of 12∘12^\circ
Big hint:
Each 3∘3^\circ drop shrinks the volume by 44 cubic centimeters
Solution:
From 32∘32^\circ to 20∘20^\circ is a 12∘12^\circ decrease, which is 44 steps of 3∘.3^\circ.
The volume decreases by 4×4=164 \times 4 = 16 cubic centimeters, from 2424 down to 24−16=8.24 - 16 = 8.
Thus, the correct answer is A .
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