2017 AMC 12B Problems/Problem 1

Problem 1

Kymbrea's comic book collection currently has $30$ comic books in it, and she is adding to her collection at the rate of $2$ comic books per month. LaShawn's collection currently has $10$ comic books in it, and he is adding to his collection at the rate of $6$ comic books per month. After how many months will LaShawn's collection have twice as many comic books as Kymbrea's?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ 25$

Solution

Kymbrea has *30* comic books initially and every month, she adds two. This can be represented as *30 + 2x* where x is the number of months elapsed. LaShawn's collection, similarly, is *10 + 6x*. To find when they will have an equal amount, we solve x for *2x + 30 = 6x + 10* and get *x = 5* $\boxed{\textbf{C}}$ .

2017 AMC 12B (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2017 AMC 12B Problems/Problem 1

Problem 1

Solution

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