Difference between revisions of "2020 AMC 12A Problems/Problem 1"
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==Solution 1== | ==Solution 1== | ||
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If Carlos took <math>70\%</math> of the pie, there must be <math>(100 - 70) = 30\%</math> left. After Maria takes <math>\frac{1}{3}</math> of the remaining <math>30\%, </math> | If Carlos took <math>70\%</math> of the pie, there must be <math>(100 - 70) = 30\%</math> left. After Maria takes <math>\frac{1}{3}</math> of the remaining <math>30\%, </math> | ||
<math>1 - \frac{1}{3} = \frac{2}{3}</math> of the remaining <math>30\%</math> is left. | <math>1 - \frac{1}{3} = \frac{2}{3}</math> of the remaining <math>30\%</math> is left. | ||
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==Solution 2== | ==Solution 2== | ||
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Like solution 1, it is clear that there is <math>30\%</math> of the pie remaining. Since Maria takes <math>\frac{1}{3}</math> of the remainder, she takes <math>\frac{1}{3} \cdot 30\% = 10\%</math> meaning that there is <math>30\% - 10\% = 20\%</math> left <math>\implies \boxed{\textbf{C}}</math>. | Like solution 1, it is clear that there is <math>30\%</math> of the pie remaining. Since Maria takes <math>\frac{1}{3}</math> of the remainder, she takes <math>\frac{1}{3} \cdot 30\% = 10\%</math> meaning that there is <math>30\% - 10\% = 20\%</math> left <math>\implies \boxed{\textbf{C}}</math>. | ||
Revision as of 07:14, 29 April 2021
Contents
Problem
Carlos took 
of a whole pie. Maria took one third of the remainder. What portion of the whole pie was left?
Solution 1
If Carlos took of the pie, there must be 
left. After Maria takes 
of the remaining 
of the remaining 
is left.
Therefore:
-Contributed by YOur dad, one dude
Solution 2
Like solution 1, it is clear that there is of the pie remaining. Since Maria takes of the remainder, she takes 
meaning that there is 
left 
.
~DBlack2021
Solution 3 (One Sentence)
We have ![\[\left(100\%-70\%\right)\cdot\left(1-\frac13\right)=30\%\cdot\frac23=\boxed{\textbf{(C)}\ 20\%}\]](http://latex.artofproblemsolving.com/0/c/e/0ce11cb93c4b54ee4c2318644ba2ce6fb8c76f81.png)
of the whole pie left.
~MRENTHUSIASM
Video Solution
~IceMatrix
See Also
| 2020 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by First Problem |
Followed by Problem 2 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
