Difference between revisions of "2022 AMC 8 Problems/Problem 9"
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+ | Alternatively, we can condense the solution above into the following equation: <math>68+(212-68)\cdot\left(\frac12\right)^{\tfrac{15}{5}}=86.</math> | ||
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~MRENTHUSIASM ~Mathfun1000 | ~MRENTHUSIASM ~Mathfun1000 | ||
Revision as of 17:03, 7 June 2022
Contents
Problem
A cup of boiling water () is placed to cool in a room whose temperature remains constant at
. Suppose the difference between the water temperature and the room temperature is halved every
minutes. What is the water temperature, in degrees Fahrenheit, after
minutes?
Solution
Initially, the difference between the water temperature and the room temperature is degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit.
After minutes, the difference between the temperatures is
degrees Fahrenheit. At this point, the water temperature is
degrees Fahrenheit.
Shorter Version
Alternatively, we can condense the solution above into the following equation:
~MRENTHUSIASM ~Mathfun1000
Video Solution
https://youtu.be/Ij9pAy6tQSg?t=627
~Interstigation
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.