2017 AMC 10B Problems/Problem 5: Difference between revisions

Revision as of 23:00, 7 October 2020

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?

$\textbf{(A)}\ 10\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 40\qquad\textbf{(E)}\ 50$

Solution

Solution 1

Denote the number of blueberry and cherry jelly beans as $b$ and $c$ respectively. Then $b = 2c$ and $b-10 = 3(c-10)$ . Substituting, we have $2c-10 = 3c-30$ , so $c=20$ , $b=\boxed{\textbf{(D) } 40}$ .

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 $\boxed{\textbf{(D) } 40}$ . We can check that 40 blueberry and 20 cherry jelly beans indeed does work.

Video Solution

https://youtu.be/QrCSysVHhPU

~savannahsolver

Video Solution by the Beauty of Math

With new whiteboard at home: https://www.youtube.com/watch?v=zTGuz6EoBWY

~icematrix

2017 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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 10 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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 ~savannahsolver
+==Video Solution by the Beauty of Math==
+With new whiteboard at home: https://www.youtube.com/watch?v=zTGuz6EoBWY
+~icematrix
 {{AMC10 box|year=2017|ab=B|num-b=4|num-a=6}}
 {{MAA Notice}}

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