Difference between revisions of "2022 AMC 8 Problems/Problem 9"
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After <math>15</math> minutes, the difference between the temperatures is <math>36\div2=18</math> degrees Fahrenheit. At this point, the water temperature is <math>68+18=\boxed{\textbf{(B) } 86}</math> degrees Fahrenheit. | After <math>15</math> minutes, the difference between the temperatures is <math>36\div2=18</math> degrees Fahrenheit. At this point, the water temperature is <math>68+18=\boxed{\textbf{(B) } 86}</math> degrees Fahrenheit. | ||
| − | + | <u><b>Remark</b></u> | |
| − | Alternatively, we can condense the solution above into the following equation: < | + | Alternatively, we can condense the solution above into the following equation: <cmath>68+(212-68)\cdot\left(\frac12\right)^{\tfrac{15}{5}}=86.</cmath> |
| + | ~MRENTHUSIASM ~MathFun1000 | ||
| − | ~ | + | ==Video Solution by Math-X (First understand the problem!!!)== |
| + | https://youtu.be/oUEa7AjMF2A?si=l1o2Qg5grdDcniVg&t=1179 | ||
| + | |||
| + | ~Math-X | ||
| + | |||
| + | ==Video Solution (CREATIVE THINKING!!!)== | ||
| + | https://youtu.be/U6L9QiKrEW0 | ||
| + | |||
| + | ~Education, the Study of Everything | ||
==Video Solution== | ==Video Solution== | ||
| − | https:// | + | https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=627 |
~Interstigation | ~Interstigation | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/1xspUFoKDnU?t=253 | ||
| + | |||
| + | ~STEMbreezy | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/XQ4nVqMrgm0 | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/0YKUSrG9G-Q | ||
| + | |||
| + | ~harungurcan | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=8|num-a=10}} | {{AMC8 box|year=2022|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 21:05, 2 January 2024
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.
Remark
Alternatively, we can condense the solution above into the following equation: ![\[68+(212-68)\cdot\left(\frac12\right)^{\tfrac{15}{5}}=86.\]](http://latex.artofproblemsolving.com/5/a/9/5a909744444c81a91c9dfe019ba59b1e1a1fa52f.png)
~MRENTHUSIASM ~MathFun1000
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/oUEa7AjMF2A?si=l1o2Qg5grdDcniVg&t=1179
~Math-X
Video Solution (CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=Ij9pAy6tQSg&t=627
~Interstigation
Video Solution
https://youtu.be/1xspUFoKDnU?t=253
~STEMbreezy
Video Solution
~savannahsolver
Video Solution
~harungurcan
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. 
