2013 AMC 10B 第 3 题

Question

一月的某一天，内布拉斯加州 Lincoln 的最高气温比最低气温高

16

度，且最高气温和最低气温的平均值为

3

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

16

degrees higher than the low temperature, and the average of the high and low temperatures was

3

degrees. What was the low temperature in Lincoln that day (in degrees)?

-13

-8

-5

-3

11

最高温和最低温围绕平均温度等距分布。

The high and low temperatures are equally spaced around the average

最低温比平均温度低

8

度。

The low temperature is

8

degrees below the average

设最低气温为

l

。则最高气温为

l+16

。

平均值满足

\dfrac{l+l+16}2 = l+8 = 3\text{。}

因此

l = -5

。

所以正确答案是 C。

Let

l

represent the low temperature. Then the high temperature is

l+16.

The average satisfies

\dfrac{l+l+16}2 = l+8 = 3.

Therefore,

l = -5.

Thus, the correct answer is C.

其他年份的第 3 题