Difference between revisions of "2023 AMC 8 Problems/Problem 10"
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* 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. | * 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. | ||
− | + | More simply, 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> | |
− | ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM | + | ~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM, CoOlPoTaToEs |
==Video Solution by Math-X (Let's first Understand the question)== | ==Video Solution by Math-X (Let's first Understand the question)== |
Revision as of 12:38, 21 January 2024
Contents
[hide]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.
- The moose ate 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.
More simply, we can condense the solution above into the following equation:
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, MRENTHUSIASM, CoOlPoTaToEs
Video Solution by Math-X (Let's first Understand the question)
https://youtu.be/Ku_c1YHnLt0?si=N3jXnFg5Zy3GCgrB&t=1500 ~Math-X
Video Solution (HOW TO THINK CREATIVELY!!!)
https://youtu.be/WKcH7Cyeipo ~Education the Study of everything
Video Solution by Magic Square
https://youtu.be/-N46BeEKaCQ?t=4814
Video Solution by Interstigation
https://youtu.be/DBqko2xATxs&t=859
Video Solution by harungurcan
https://www.youtube.com/watch?v=oIGy79w1H8o&t=246s
Video Solution by SpreradTheMathLove
https://www.youtube.com/watch?v=TAa6jarbATE
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.