AMC 8 1991 Problem 21
AMC8 1991 年第 21 题
数列与规律★★★☆☆
For every 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 , what was the volume of the gas in cubic centimeters when the temperature was ?
温度每升高 ，某气体的体积膨胀 4 立方厘米。如果温度为 时气体体积为 24 立方厘米，则温度为 时气体体积是多少立方厘米？
- A.8
- B.12
- C.15
- D.16
- E.40
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
The temperature increased by , so it increased by four times. Since each increase caused the volume of the gas to expand by 4 cubic centimeters, the gas expanded by a total of cubic centimeters. Therefore, the original volume of the gas was 24 - 16 = 8 cubic centimeters.
Let be the temperature in degrees and be the volume of the gas. Since a increase in the temperature causes a 4 cubic centimeter expansion, the relationship between and is linear and has slope . Using point-slope form with the point (32, 24), the equation of this relationship is . Substituting x = 20 gives y = 8.
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