2014 AMC 10B Problem 4

Below is the professionally curated solution for Problem 4 of the 2014 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10B solutions, or check the answer key.

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Concepts:system of equations ratio and proportion

Difficulty rating: 960

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?

$\dfrac{3}{2}$

$\dfrac{5}{3}$

$\dfrac{7}{4}$

$2$

$\dfrac{13}{4}$

Solution:

Let the price for a muffin be $m$ and let the price for a banana be $b.$ Then, $\begin{align*} 2(4m+3b) &= 16b + 2m\\ 8m+6b &= 16b + 2m \\ 10b &= 6m\\ m &= \dfrac 53 b.\end{align*}$

Thus, the correct answer is B .

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