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2023 AMC 8 Problems/Problem 10: Difference between revisions

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==Solution 1==  
==Problem==


Harold made a plum pie. We can distribute into different fractions of pie that the animals ate. First Harold ate <math>\frac{1}{4}</math> of the pie and the remains are <math>\frac{3}{4}</math> of the pie. From this a moose comes and eats <math>\frac{3}{4} * \frac{1}{3}</math> and what remains is <math>\frac{3}{4} - \frac{1}{4} = \frac{1}{2}</math>. From this a porcupine comes and eat <math>\frac{1}{3} * \frac{1}{2} = \frac{1}{6}</math> and our final answer of what remains is <math>\frac{1}{2} - \frac{1}{6} =  \boxed{\text{(D)}\frac{1}{3}}</math>.  
Harold made a plum pie to take on a picnic. He was able to eat only <math>\frac{1}{4}</math> of the pie, and he left the rest for his friends. A moose came by and ate <math>\frac{1}{3}</math> of what Harold left behind. After that, a porcupine ate <math>\frac{1}{3}</math> of what the moose left behind. How much of the original pie still remained after the porcupine left?


<math>\textbf{(A)}\ \frac{1}{12} \qquad \textbf{(B)}\ \frac{1}{6} \qquad \textbf{(C)}\ \frac{1}{4} \qquad \textbf{(D)}\ \frac{1}{3} \qquad \textbf{(E)}\ \frac{5}{12}</math>


~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, lpieleanu
==Solution==
 
Note that:
 
 
 
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>
 
~apex304, SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, lpieleanu, MRENTHUSIASM
 
==See Also==
{{AMC8 box|year=2023|num-b=9|num-a=11}}
{{MAA Notice}}

Revision as of 23:25, 24 January 2023

Problem

Harold made a plum pie to take on a picnic. He was able to eat only $\frac{1}{4}$ of the pie, and he left the rest for his friends. A moose came by and ate $\frac{1}{3}$ of what Harold left behind. After that, a porcupine ate $\frac{1}{3}$ of what the moose left behind. How much of the original pie still remained after the porcupine left?

$\textbf{(A)}\ \frac{1}{12} \qquad \textbf{(B)}\ \frac{1}{6} \qquad \textbf{(C)}\ \frac{1}{4} \qquad \textbf{(D)}\ \frac{1}{3} \qquad \textbf{(E)}\ \frac{5}{12}$

Solution

Note that:


Alternatively, we can condense the solution above into the following equation: \[\left(1-\frac14\right)\left(1-\frac13\right)\left(1-\frac13\right) = \frac34\cdot\frac23\cdot\frac23 = \frac13.\]

~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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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