Difference between revisions of "2012 AMC 8 Problems/Problem 4"
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Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat? | Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat? | ||
− | <math> \textbf{(A)} | + | <math> \textbf{(A)}~\frac{1}{24}\qquad\textbf{(B)}~\frac{1}{12}\qquad\textbf{(C)}~\frac{1}{8}\qquad\textbf{(D)}~\frac{1}{6}\qquad\textbf{(E)}~\frac{1}{4} </math> |
− | ==Solution== | + | ==Solution 1== |
− | Peter ate <math>1 + \frac{1}{2} = \frac{3}{2}</math> slices. The pizza has <math> 12 </math> slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peter ate <math>\boxed{\textbf{(C)}\ \frac{1}{8}}</math> of the pizza. | + | Peter ate <math>1 + \frac{1}{2} = \frac{3}{2}</math> slices. The pizza has <math> 12 </math> slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peter ate <math>\dfrac{\frac{3}{2}\text{ slices}}{12\text{ slices}} = \boxed{\textbf{(C)}\ \frac{1}{8}}</math> of the pizza. |
+ | |||
+ | ==Solution 2== | ||
+ | An alternative way of solving this problem is to add the slices separately. When Peter takes a full slice, he takes <math>\frac{1}{12}</math> of the pizza. When he shares the slice with paul, he splits a slice of pizza into two, the equation is <math>\frac{1}{2}</math> of <math>\frac{1}{12}</math>, which is <math>\frac{1}{24}</math>. Adding gives: <cmath>\frac{1}{12}+\frac{1}{24}=\boxed{\textbf{(C)}~\frac{1}{8}}</cmath> | ||
+ | |||
+ | ~SmartGrowth ~edited by megaboy6679 | ||
+ | |||
+ | ==Solution 3== | ||
+ | Just like the above solutions, we know that Peter ate <math>\frac{3}{2}</math> slices, which is just 1.5 in decimals. There are 12 slices in total, so the fraction would be <math>\frac{1.5}{12}</math>. To remove the decimal, we can multiply it by 2 to get <math>\frac{3}{24}</math> , which is just <math>\boxed{\textbf{(C)}\ \frac{1}{8}}</math> of the pizza. | ||
+ | |||
+ | ~AhmetAcreOfLand | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/WDRPwoRbpKo ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2012|num-b=3|num-a=5}} | {{AMC8 box|year=2012|num-b=3|num-a=5}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 18:19, 30 June 2025
Problem
Peter's family ordered a 12-slice pizza for dinner. Peter ate one slice and shared another slice equally with his brother Paul. What fraction of the pizza did Peter eat?
Solution 1
Peter ate slices. The pizza has
slices total. Taking the ratio of the amount of slices Peter ate to the amount of slices in the pizza, we find that Peter ate
of the pizza.
Solution 2
An alternative way of solving this problem is to add the slices separately. When Peter takes a full slice, he takes of the pizza. When he shares the slice with paul, he splits a slice of pizza into two, the equation is
of
, which is
. Adding gives:
~SmartGrowth ~edited by megaboy6679
Solution 3
Just like the above solutions, we know that Peter ate slices, which is just 1.5 in decimals. There are 12 slices in total, so the fraction would be
. To remove the decimal, we can multiply it by 2 to get
, which is just
of the pizza.
~AhmetAcreOfLand
Video Solution
https://youtu.be/WDRPwoRbpKo ~savannahsolver
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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.