PS 1000: Section 7 #17

[envyk10]

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

[bww]

Hi...is answer 8/3?

Ok, let's assume that it is. So we have 4 cups of milk that need to be poured into a total capacity of 6 cups (from 2 cup bottle and 4 cup bottle). 4/6 gives us 2/3, so we know that the 4 cups poured between the two bottles will fill 2/3 of the two capacities. 2/3 will be the same fraction for both cups, as stated in the question.

2/3 of 2 cups=4/3
2/3 of 4 cups=8/3

Double-check: There will be 4/3 cups of milk poured into the 2 cup bottle, and 8/3 cups poured into the 4 cup bottle. Together, 4/3+8/3=12/3 or 4 cups.

[envyk10]

Yes, 8/3 is the correct answer

[ns88]

let x be the cups of milk to the 2 cup

then 4-x to the 4 cup

x/2=4-x/4

x=4/3

4-4/3= 8/3

[Cybermusings]

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

4-cup bottle ----
1 cup --- 1/4 capacity
2/3 cup ---- 1/4 * 2/3 = 1/6 cpacity
4-2/3 = (12-2)/3 = 10/3 cups in 2 cup bottle = 5/3 capacity

B) 7/3 cups in 4-cup bottle = 1/4*7/3 = 7/12 capcity
4-7/3 = 5/3 cups in 2 cup bottle = 1/2 * 5/3 = 5/6 capacity

C) 5/2 cups in 4 cup bottle = 1/4 * 5/2 = 5/8 capcity
4-5/2 = 3/2 cups in 2 cup bottle = 1/2 * 3/2 = 3/4 capcity

D) 8/3 cups in 4 cup botthe = 1/4*8/3 = 2/3 capcity
4-8/3 = 4/3 cups = 1/2 * 4/3 = 4/6 = 2/3 capcity

Hence D