Difference between revisions of "2014 AMC 10B Problems/Problem 4"

Latest revision as of 21:36, 26 September 2023

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 $m$ be the cost of a muffin and $b$ be the cost of a banana. From the given information, $2m+16b=2(4m+3b)=8m+6b\Rightarrow 10b=6m\Rightarrow m=\frac{10}{6}b=\boxed{\frac{5}{3}\rightarrow \text{(B)}}$ .

Video Solution (CREATIVE THINKING)

https://youtu.be/_AvJzq4QiUg

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Video Solution

https://youtu.be/7_-ZvunSC8w

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2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AMC 10 Problems and Solutions

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

@@ Line 6: / Line 6: @@
 ==Solution==
-Let <math>m</math> be the cost of a muffin and <math>b</math> be the cost of a banana. From the given information, <cmath>2m+16b=2(4m+3b)=8m+6b\Rightarrow 10b=6m\Rightarrow m=\frac{10}{6}b=\text{(B) } \boxed{\frac{5}{3}\rightarrow \text{B}}</cmath>.
+Let <math>m</math> be the cost of a muffin and <math>b</math> be the cost of a banana. From the given information, <cmath>2m+16b=2(4m+3b)=8m+6b\Rightarrow 10b=6m\Rightarrow m=\frac{10}{6}b=\boxed{\frac{5}{3}\rightarrow \text{(B)}}</cmath>.
 ==Video Solution (CREATIVE THINKING)==

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