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Algebra Difficulty 2.9 Junior Find the answer

At noon on a certain day, Minneapolis is NN degrees warmer than St. Louis. At 4:004{:}00 the temperature in Minneapolis has fallen by 55 degrees while the temperature in St. Louis has risen by 33 degrees, at which time the temperatures in the two cities differ by 22 degrees. What is the product of all possible values of N?N?

Pick one

Solution

At noon on a certain day, let MM and LL be the temperatures (in degrees) in Minneapolis and St. Louis, respectively. It follows that M=L+N.M=L+N.
At 4:00,4{:}00, we get
\begin{align*} |(M-5)-(L+3)| &= 2 \\ |M-L-8| &= 2 \\ |N-8| &= 2. \end{align*}
We have two cases:

If N−8=2,N-8=2, then N=10.N=10.
If N−8=−2,N-8=-2, then N=6.N=6.

Together, the product of all possible values of NN is 10⋅6=(C) 60.10\cdot6=\boxed{\textbf{(C)} \: 60}.
~Wilhelm Z ~KingRavi ~MRENTHUSIASM

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.