Problem Solving

Hi Vincen,

We're told that four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle and that each bottle is to be filled to the SAME fraction of its capacity. We're asked for the number of cups of milk that will be poured into the 4-cup bottle.

The total volume of the 2 bottles is 6 cups. The 4 cups of milk would fill 4/6 = 2/3 of that capacity; thus, each bottle would have to be filled to 2/3 of its capacity.

2/3 of the 4-cup bottle would be (2/3)(4) = 8/3 cups

Final Answer: D

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Rich

Vincen wrote:Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle?

(A) 2/3
(B) 7/3
(C) 5/2
(D) 8/3
(E) 3

If we let the amount of milk poured into the 2-cup bottle = n, then the amount poured into the 4-cup bottle is 4 - n; thus:

n/2 = (4- n)/4

4n = 2(4 - n)

4n = 8 - 2n

6n = 8

n = 8/6 = 4/3 = 1 1/3

The amount poured into the 4-cup bottle is 4 - 1 1/3 = 2 2/3 = 8/3.

Answer D