2021 AMC 10 B Fall
Complete problem set with solutions and individual problem pages
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 ?(2021 AMC Fall 10B, Question #4)
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Solution 1:
At noon on a certain day, let and be the temperatures (in degrees) in Minneapolis and St. Louis, respectively. It follows that . At , we get We have two cases: 1. If , then . 2. If , then . Together, the product of all possible values of is .
Solution 2:
At noon on a certain day, the difference of temperatures in Minneapolis and St. Louis is degrees.
At , the difference of temperatures in Minneapolis and St. Louis is degrees. It follows that We continue with the casework in Solution 1 to get the answer .
