2023 AMC 8 Problems/Problem 10
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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
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4814
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. 
