2014 AMC 10B Problem 4

Problem 4 of 25EasierAlgebra

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?

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Solution

Let the price for a muffin be

m

and let the price for a banana be

b.

Then,

\begin{aligned} 2(4m+3b) &= 16b + 2m\\ 8m+6b &= 16b + 2m \\ 10b &= 6m\\ m &= \dfrac 53 b.\end{aligned}

Thus, the correct answer is B .

Concepts: system of equations · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.