Difference between revisions of "2014 AMC 12B Problems/Problem 4"

Revision as of 12:35, 24 January 2015

Problem

Susie pays for $4$ muffins and $3$ bananas. Calvin spends twice as much paying for $2$ muffins and $16$ 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 $m$ stand for the cost of a muffin, and let $b$ stand for the value of a banana. We we need to find $\frac{m}{b}$ , the ratio of the price of the muffins to that of the bananas. We have $2(4m + 3b) = 2m + 16b$ $6m = 10b$ $\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}$

2014 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 3: / Line 3: @@
 Susie pays for <math> 4 </math> muffins and <math> 3 </math> bananas. Calvin spends twice as much paying for <math> 2 </math> muffins and <math> 16 </math> bananas. A muffin is how many times as expensive as a banana?
-<cmath> \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} </cmath>
+<math> \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} </math>
 ==Solution==

Page

Toolbox

Search

Difference between revisions of "2014 AMC 12B Problems/Problem 4"

Revision as of 12:35, 24 January 2015

Problem

Solution

See also