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

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==Solution==
 
==Solution==
  
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Let <math>m</math> stand for the cost of a muffin, and let <math>b</math> stand for the value of a banana. We we need to find <math>\frac{m}{b}</math>, the ratio of the price of the muffins to that of the bananas. We have
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Let <math>m</math> stand for the cost of a muffin, and let <math>b</math> stand for the value of a banana. We need to find <math>\frac{m}{b}</math>, the ratio of the price of the muffins to that of the bananas. We have
 
<cmath>2(4m + 3b) = 2m + 16b </cmath>
 
<cmath>2(4m + 3b) = 2m + 16b </cmath>
 
<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>
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==Video Solution 1 (Quick and Easy)==
 
==Video Solution 1 (Quick and Easy)==

Latest revision as of 18:30, 17 October 2024

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?

$\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{7}{4}\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{13}{4}$

Solution

Let $m$ stand for the cost of a muffin, and let $b$ stand for the value of a banana. We need to find $\frac{m}{b}$, the ratio of the price of the muffins to that of the bananas. We have \[2(4m + 3b) = 2m + 16b\] \[6m = 10b\] \[\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}\]

Video Solution 1 (Quick and Easy)

https://youtu.be/K4HupKj78Yc

~Education, the Study of Everything

See also

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

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