Difference between revisions of "2017 AMC 10B Problems/Problem 5"
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<math>\textbf{(A)}\ 10\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 40\qquad\textbf{(E)}\ 50</math> | <math>\textbf{(A)}\ 10\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 40\qquad\textbf{(E)}\ 50</math> | ||
| − | ==Solution 1== | + | ==Solution== |
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| + | ===Solution 1=== | ||
Denote the number of blueberry and cherry jelly beans as <math>b</math> and <math>c</math> respectively. Then <math>b = 2c</math> and <math>b-10 = 3(c-10)</math>. Substituting, we have <math>2c-10 = 3c-30</math>, so <math>c=20</math>, <math>b=\boxed{\textbf{(D) } 40}</math>. | Denote the number of blueberry and cherry jelly beans as <math>b</math> and <math>c</math> respectively. Then <math>b = 2c</math> and <math>b-10 = 3(c-10)</math>. Substituting, we have <math>2c-10 = 3c-30</math>, so <math>c=20</math>, <math>b=\boxed{\textbf{(D) } 40}</math>. | ||
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| + | ===Solution 2=== | ||
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| + | From the problem, we see that 10 less than one of the answer choices must be a multiple of 3 and positive. The only answer choice satisfying this is <math>\boxed{\textbf{(D) } 40}</math>. We can check that 40 blueberry and 20 cherry jelly beans indeed does work. | ||
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| + | {{AMC10 box|year=2017|ab=B|num-b=4|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 10:12, 26 July 2017
Contents
Problem
Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?
Solution
Solution 1
Denote the number of blueberry and cherry jelly beans as 
and 
respectively. Then 
and 
. Substituting, we have 
, so 
, 
.
Solution 2
From the problem, we see that 10 less than one of the answer choices must be a multiple of 3 and positive. The only answer choice satisfying this is 
. We can check that 40 blueberry and 20 cherry jelly beans indeed does work.
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
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| All AMC 10 Problems and Solutions | ||
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