2021 Fall AMC 12B Problems/Problem 3
- The following problem is from both the 2021 Fall AMC 10B #4 and 2021 Fall AMC 12B #3, so both problems redirect to this page.
Contents
Problem
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 1 (Two Variables)
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:
- If then
- If then
Together, the product of all possible values of is
~Wilhelm Z ~KingRavi ~MRENTHUSIASM
Solution 2 (One Variable)
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
~Steven Chen (www.professorchenedu.com) ~MRENTHUSIASM
Video Solution by Interstigation
https://youtu.be/p9_RH4s-kBA?t=291
~Interstigation
Video Solution
~Education, the Study of Everything
Video Solution by WhyMath
~savannahsolver
Video Solution by TheBeautyofMath
For AMC 10: https://youtu.be/lC7naDZ1Eu4?t=670
For AMC 12: https://youtu.be/yaE5aAmeesc?t=379
~IceMatrix
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.