Fractions

[Nycgrl]

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


OA = D

[newera]

2 cups + 4 cups = total of 6 cups

so the 2 cup bottle is 1/3 total cups and the 4 cup bottle is 2/3 total cups.

If we pour one cup of milk in the 2 cup bottle, thats already at half capacity. Equally, 2 cups of milk in the 4 cup bottle. Now you're left with one cup that needs to be distributed. Just refer back to the original breakdown mentioned about.

so 2/3 of that last cup of milk will go to the bigger bottle. Total is 2 2/3 cups. or 8/3 cups, which is D

[rey.fernandez]

newera's solution is great -- nice way to reason your way through without too much hassle.

Here's an algebraic approach:

let x be the fraction of each bottle's capacity that is to be filled. So,

2x + 4x = 4
6x = 4
x = 2/3

So each bottle should be filled to 2/3 of its capacity. The 4-cup bottle will be filled with 4(2/3) = 8/3 cups.

[eccentric]

The key here is the cup of milk must be distributed as the ratio of the volume of bottles which is 2:4 ---> 1:2

2/3 = x/4 { part and whole }
hence x = 8/3

Regards,
eccentric