Difference between revisions of "2023 AMC 8 Problems/Problem 10"
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| − | * Harold ate <math>\frac14</math> of the pie. After that, <math>1-\frac14 = \frac34</math> of the pie was left. | + | * Harold ate <math>\frac14</math> of the pie. After that, <math>1-\frac14=\frac34</math> of the pie was left behind. |
| − | * The moose ate <math>\frac13\cdot\frac34 = \frac14</math> of the pie. After that, <math>\frac34 - \frac14 = \frac12</math> of the pie was left. | + | * The moose ate <math>\frac13\cdot\frac34 = \frac14</math> of the pie. After that, <math>\frac34 - \frac14 = \frac12</math> of the pie was left behind. |
| − | * The porcupine ate <math>\frac13\cdot\frac12 = \frac16</math> of the pie. After that, <math>\frac12 - \frac16 = \boxed{\textbf{(D)}\ \frac{1}{3}}</math> of the pie was left. | + | * The porcupine ate <math>\frac13\cdot\frac12 = \frac16</math> of the pie. After that, <math>\frac12 - \frac16 = \boxed{\textbf{(D)}\ \frac{1}{3}}</math> of the pie was left behind. |
Alternatively, we can condense the solution above into the following equation: <cmath>\left(1-\frac14\right)\left(1-\frac13\right)\left(1-\frac13\right) = \frac34\cdot\frac23\cdot\frac23 = \frac13.</cmath> | Alternatively, we can condense the solution above into the following equation: <cmath>\left(1-\frac14\right)\left(1-\frac13\right)\left(1-\frac13\right) = \frac34\cdot\frac23\cdot\frac23 = \frac13.</cmath> | ||
Revision as of 23:53, 24 January 2023
Problem
Harold made a plum pie to take on a picnic. He was able to eat only 
of the pie, and he left the rest for his friends. A moose came by and ate 
of what Harold left behind. After that, a porcupine ate of what the moose left behind. How much of the original pie still remained after the porcupine left?
Solution
Note that:
- Harold ate
of the pie. After that, 
of the pie was left behind.
of the pie. After that, 
of the pie was left behind.- The moose ate
of the pie. After that, 
of the pie was left behind.
of the pie. After that, 
of the pie was left behind.- The porcupine ate
of the pie. After that, 
of the pie was left behind.
of the pie. After that, 
of the pie was left behind.Alternatively, we can condense the solution above into the following equation: ![\[\left(1-\frac14\right)\left(1-\frac13\right)\left(1-\frac13\right) = \frac34\cdot\frac23\cdot\frac23 = \frac13.\]](http://latex.artofproblemsolving.com/b/7/9/b79c7d75d940ecb0d045b002bc7f0e20a2bafa3e.png)
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, lpieleanu, MRENTHUSIASM
See Also
| 2023 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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. 
