2014 AMC 12B 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 a muffin cost

m

and a banana cost

b.

Then

2(4m+3b) = 2m+16b.

Expanding gives

8m+6b = 2m+16b,

6m = 10b

and

m = \tfrac53 b.

Thus, the correct answer is B.

Concepts: linear equation · ratio and proportion

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