Difference between revisions of "2014 AMC 12B Problems/Problem 4"
Kevin38017 (talk | contribs) (→Solution) |
Kevin38017 (talk | contribs) |
||
| Line 11: | Line 11: | ||
<cmath>6m = 10b </cmath> | <cmath>6m = 10b </cmath> | ||
<cmath>\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}</cmath> | <cmath>\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}</cmath> | ||
| − | |||
| − | |||
Revision as of 21:35, 20 February 2014
Problem
Susie pays for 
muffins and 
bananas. Calvin spends twice as much paying for 
muffins and 
bananas. A muffin is how many times as expensive as a banana?
$\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{7}{4}\qquad\textbf{(D)}}\ 2\qquad\textbf{(E)}\ \frac{13}{4}$ (Error compiling LaTeX. Unknown error_msg)
Solution
Let 
stand for the cost of a muffin, and let 
stand for the value of a banana. We we need to find 
, the ratio of the price of the muffins to that of the bananas. We have
![\[2(4m + 3b) = 2m + 16b\]](http://latex.artofproblemsolving.com/c/4/a/c4a833d68798cfa8c0721f1d738a16f24eedd2a7.png)
![\[6m = 10b\]](http://latex.artofproblemsolving.com/a/f/0/af0c19a2db3a0a83db506a7d8815b4843e953fc3.png)
![\[\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}\]](http://latex.artofproblemsolving.com/0/a/f/0af7e28cf6bbd335cd902c6031b410b54dc11e03.png)
