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Difference between revisions of "2017 AMC 12B Problems/Problem 1"
 
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==Problem 1==
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==Problem==
  
 
Kymbrea's comic book collection currently has <math>30</math> comic books in it, and she is adding to her collection at the rate of <math>2</math> comic books per month. LaShawn's collection currently has <math>10</math> comic books in it, and he is adding to his collection at the rate of <math>6</math> comic books per month. After how many months will LaShawn's collection have twice as many comic books as Kymbrea's?
 
Kymbrea's comic book collection currently has <math>30</math> comic books in it, and she is adding to her collection at the rate of <math>2</math> comic books per month. LaShawn's collection currently has <math>10</math> comic books in it, and he is adding to his collection at the rate of <math>6</math> comic books per month. After how many months will LaShawn's collection have twice as many comic books as Kymbrea's?
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==Solution==
 
==Solution==
  
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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* <math>\boxed{\textbf{C}}</math>.
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Kymbrea has <math>30</math> comic books initially and every month, she adds two. This can be represented as <math>30 + 2x</math> where x is the number of months elapsed. LaShawn's collection, similarly, is <math>10 + 6x</math>. To find when LaShawn will have twice the number of comic books as Kymbrea, we solve for x with the equation <math>2(2x + 30) = 6x + 10</math> and get <math>x = \boxed{\textbf{(E) } 25}</math>.
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==See Also==
 
==See Also==
 
{{AMC12 box|year=2017|ab=B|before=First Problem|num-a=2}}
 
{{AMC12 box|year=2017|ab=B|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}
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[[Category:Introductory Algebra Problems]]

Latest revision as of 12:51, 15 February 2021

Problem

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 LaShawn will have twice the number of comic books as Kymbrea, we solve for x with the equation $2(2x + 30) = 6x + 10$ and get $x = \boxed{\textbf{(E) } 25}$.

See Also

2017 AMC 12B (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

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