2014 AMC 12B Problem 4

Attempt Problem 4 of the 2014 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 12B solutions, or check the answer key.

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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?

$\dfrac{3}{2}$

$\dfrac{5}{3}$

$\dfrac{7}{4}$

$2$

$\dfrac{13}{4}$

Answer: B

Concepts:linear equation ratio and proportion

Difficulty rating: 1230

Solution:

Let a muffin cost $m$ and a banana cost $b.$ Then $2(4m+3b) = 2m+16b.$

Expanding gives $8m+6b = 2m+16b,$ so $6m = 10b$ and $m = \tfrac53 b.$

Thus, the correct answer is B.

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