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Cups of milk [#permalink] New post 13 Sep 2007, 18:36
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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
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 [#permalink] New post 13 Sep 2007, 21:39
I believe the answer is 8/3 (D)

x/4 = (4-x)/2
x = 2(4-x) = 8-2x
x = 8/3

so 8/3 into 4 cup bottle... ratio is 8/3/4 = 8/12 = 2/3
and 4-8/3 = 4/3 into 2 cup bottle..ratio is 4/3/2 = 4/6 = 2/3

also, 8/3 + 4/3 = 12/3 = 4 cups


answer can't be A because if 2/3 cup goes into the 4 cup then 4-2/3 = 10/3 cup would need to go into a 2 cup bottle....
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 [#permalink] New post 13 Sep 2007, 21:47
CalSpeedRacer wrote:
I believe the answer is 8/3 (D)

x/4 = (4-x)/2
x = 2(4-x) = 8-2x
x = 8/3

so 8/3 into 4 cup bottle... ratio is 8/3/4 = 8/12 = 2/3
and 4-8/3 = 4/3 into 2 cup bottle..ratio is 4/3/2 = 4/6 = 2/3

also, 8/3 + 4/3 = 12/3 = 4 cups


answer can't be A because if 2/3 cup goes into the 4 cup then 4-2/3 = 10/3 cup would need to go into a 2 cup bottle....


Actually we found the value of x (Fraction of the capacity of bottles) which is equal to 2/3.
However in the question, it is asked that "how many cups of milk should be poured into the 4-cup bottle"

So the answer should be x of 4
= x* 4
= 2/3 *4
= 8/3

hence D.

- Brajesh
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 [#permalink] New post 14 Sep 2007, 07:13
I also got D

I said: x + y = 4 (i.e. x is the amount to be poured into the 2 cup bottle and y is the amount to be poured into the 4 cup bottle)

Then, x/2 = y/4 (ie. the amount to be poured into the 2 cup bottle is the same fraction of its capacity as the amount to be poured into the 4 cup holder)

Then I solved the simultaneous equations

x+y=4
x/2 = y/4


i.e. x/2 = y/4 becomes x = 2y/4.........then x =y/2

then I plugged y/2 for x in the equation x+y = 4
which becomes y/2 + y = 4.....then 3y =8 ...then y=8/3

y represents the amount poured into the 4 cup bottle, therefore answer is D
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 [#permalink] New post 14 Sep 2007, 22:09
CalSpeedRacer wrote:
I believe the answer is 8/3 (D)

x/4 = (4-x)/2
x = 2(4-x) = 8-2x
x = 8/3

so 8/3 into 4 cup bottle... ratio is 8/3/4 = 8/12 = 2/3
and 4-8/3 = 4/3 into 2 cup bottle..ratio is 4/3/2 = 4/6 = 2/3

also, 8/3 + 4/3 = 12/3 = 4 cups


answer can't be A because if 2/3 cup goes into the 4 cup then 4-2/3 = 10/3 cup would need to go into a 2 cup bottle....
using CalSpeed's method, if I were to do this:

4-x/4 = x/2 Iget x = 4/3. why doesn't this equation work? isn't it saying the same as the above?
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Re: Cups of milk [#permalink] New post 14 Sep 2007, 22:59
Fistail wrote:
b14kumar wrote:
ggarr 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


Is it A?

- Brajesh

yup.

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


was bit hasty..........................

2 cup bottle: 2/3 of 2 cups = 4/3
4 cup bottle: 2/3 of 4 cups = 8/3
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 [#permalink] New post 15 Sep 2007, 07:25
I did this question today, it is taken from PS 1000, am I right???

AO is D
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Re: Cups of milk [#permalink] New post 17 Sep 2007, 21:10
ggarr 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


This is how I read to solve the problem. The cup only confuses:

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

Now milk added to fill 2x+4x = 6x = 4 => x= 2/3
Milk poured in 4-cup ( gallon) bottle = 4x = 8/3
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 [#permalink] New post 17 Sep 2007, 21:20
pretty straightforward guys.

2 cup + 4 cup = 6 cups of empty bottle
you have 4 cups of milk

4/6 = 2/3 so each one will be filled to 2/3 of capacity.

2/3(4) = 8/3

D. 8/3
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 [#permalink] New post 17 Sep 2007, 21:55
Bottle A - 2 cup bottle
Bottle B - 4 cup bottle

A/B = 1/2

# of cups into B = 2/3 * 4 = 8/3
  [#permalink] 17 Sep 2007, 21:55
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