Difference between revisions of "2021 Fall AMC 10B Problems/Problem 4"
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Let the temperature of Minneapolis at noon be <math>M</math> and let the temperature of St. Louis at noon be <math>S</math>. Then <math>M = N + S</math> and <math>(M-5)-(S+3) = |2| \implies M-S-8 = |2|</math>. | Let the temperature of Minneapolis at noon be <math>M</math> and let the temperature of St. Louis at noon be <math>S</math>. Then <math>M = N + S</math> and <math>(M-5)-(S+3) = |2| \implies M-S-8 = |2|</math>. | ||
− | Substituting <math>M</math> into the second equation we have <math>N - 8 | + | Substituting <math>M</math> into the second equation we have <math>N - 8 = |2| \implies N = 10, 6</math>. |
− | The product of all possible values of N is therefore < | + | The product of all possible values of N is therefore <math>10\cdot6=60=\boxed{C}</math> |
~KingRavi | ~KingRavi |
Revision as of 00:49, 23 November 2021
At noon on a certain day, Minneapolis is degrees warmer than St. Louis. At
the temperature in Minneapolis has fallen by
degrees while the temperature in St. Louis has risen by
degrees, at which time the temperatures in the two cities differ by
degrees. What is the product of all possible values of
Solution
Let the temperature of Minneapolis at noon be and let the temperature of St. Louis at noon be
. Then
and
.
Substituting into the second equation we have
.
The product of all possible values of N is therefore
~KingRavi