Difference between revisions of "2022 AMC 8 Problems/Problem 9"
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<math>\textbf{(A) } 77 \qquad \textbf{(B) } 86 \qquad \textbf{(C) } 92 \qquad \textbf{(D) } 98 \qquad \textbf{(E) } 104</math> | <math>\textbf{(A) } 77 \qquad \textbf{(B) } 86 \qquad \textbf{(C) } 92 \qquad \textbf{(D) } 98 \qquad \textbf{(E) } 104</math> | ||
− | ==Solution== | + | ==Solution 1== |
− | Initially, the difference between the water temperature and the room temperature is <math>212-68=144</math> degrees Fahrenheit. | + | Initially, the difference between the water temperature and the room temperature is <math>212-68=144^{\circ}\text{F}</math>. After <math>15</math> minutes, the difference would be decreased by a factor of <math>2^{\tfrac{15}{3}}=8</math>. Now, the difference is <math>144\div8=18^{\circ}\text{F}</math>. Finally, the water temperature is <math>68+18=\boxed{\textbf{(B) } 86}</math> degrees Fahrenheit. |
− | + | ~MRENTHUSIASM | |
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− | ~ | + | ~MathFun1000 (Conciseness) |
==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}} |
Revision as of 18:11, 28 January 2022
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 1
Initially, the difference between the water temperature and the room temperature is . After
minutes, the difference would be decreased by a factor of
. Now, the difference is
. Finally, the water temperature is
degrees Fahrenheit.
~MRENTHUSIASM
~MathFun1000 (Conciseness)
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.