2013 AMC 10B 第 3 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

3.

一月的某一天,内布拉斯加州 Lincoln 的最高气温比最低气温高 1616 度,且最高气温和最低气温的平均值为 33 度。那天 Lincoln 的最低气温是多少度?

On a particular January day, the high temperature in Lincoln, Nebraska, was 1616 degrees higher than the low temperature, and the average of the high and low temperatures was 33 degrees. What was the low temperature in Lincoln that day (in degrees)?

13-13

8-8

5-5

3-3

1111

答案:C
知识点:平均数一次方程
难度评级:560
解答:

设最低气温为 ll。则最高气温为 l+16l+16

平均值满足 因此 l=5l = -5l+l+162=l+8=3. \dfrac{l+l+16}2 = l+8 = 3.

所以正确答案是 C

Let the low temperature be represented by l.l. Then, the high temperature is l+16.l+16.

This makes the average l+l+162=l+8=3. \dfrac{l+l+16}2 = l+8 = 3. Therefore, l=5.l = -5.

Thus, the correct answer is C .

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