2013 AMC 10B Problem 3

Question

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

The high and low temperatures are equally spaced around the average

The low temperature is

8

degrees below the average

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.

Problem 3 in other years