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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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}

Let a muffin cost

m

and a banana cost

b

Calvin spending twice as much means

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

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.

Problem 4 in other years