1991 AMC 8 Problem 21

Below is the professionally curated solution for Problem 21 of the 1991 AMC 8, 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.

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Concepts:rate work backwards

Difficulty rating: 950

21.

For every $3^\circ$ 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 $32^\circ,$ what was the volume of the gas in cubic centimeters when the temperature was $20^\circ?$

$8$

$12$

$15$

$16$

$40$

Solution:

From $32^\circ$ to $20^\circ$ is a $12^\circ$ decrease, which is $4$ steps of $3^\circ.$

The volume decreases by $4 \times 4 = 16$ cubic centimeters, from $24$ down to $24 - 16 = 8.$

Thus, the correct answer is A .

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