2021 Fall AMC 10B Problem 4

Problem 4 of 25EasierAlgebra

At noon on a certain day, Minneapolis is

N

degrees warmer than St. Louis. At

4{:}00

the temperature in Minneapolis has fallen by

5

degrees while the temperature in St. Louis has risen by

3

degrees, at which time the temperatures in the two cities differ by

2

degrees. What is the product of all possible values of

N?

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Solution

Let

N=m-s

be the noon temperature difference. At

4{:}00,

the new difference is

(m-5)-(s+3)=N-8.

The temperatures then differ by

2

degrees, so

|N-8|=2.

Hence

N=6

N=10,

and the product of all possible values is

6\cdot10=60.

Thus, the answer is C .

Tagged: absolute value · linear equation