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The contents of bottle of wine that is 80% full can be

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kevincan
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The contents of bottle of wine that is 80% full can be [#permalink] New post   02 Oct 2006, 04:04
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The contents of bottle of wine that is 80% full can be emptied into 9 identical glasses so that each glass is ¾ full. How many identical, completely full bottles would be needed to completely fill 75 such glasses?

(A) 5 (B) 6 (C) 7 (D) 8 (E) more than 8



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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   02 Oct 2006, 10:09
The contents of bottle of wine that is 80% full can be emptied into 9 identical glasses so that each glass is ¾ full. How many identical, completely full bottles would be needed to completely fill 75 such glasses?

let the contents be 720 ml 80% = 576

devided on 9 galsses = 64

64 is 3/4 of each galss thus 64*4/3

75 glass will be filled with 64*4/3 *75 = 6400

6400/720 = 8.89

thus E is my answer
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   03 Oct 2006, 02:30
sorry made a calculation mistake, answer must be E

agree
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 09:58
It is E......

Hey kevin, isn't it a simple one?
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 14:27
E

80% fills 3/4 of 9
need extra 1/4 to fill them:
5/4 * 80 = 100
so 1 full fills 9 completely

72 = 8*9 so 75 > 8
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 15:43
let the big bottle be X, and small bottle be Y
80% X=75%*9Y
(4/5)X=(27/4)Y
X/Y=(27/4)/(4/5)
X/Y=(27*5)/(4*4)
therefore
75Y=75*(16)X/(27*5)
75Y=80X/9
75Y=8.8X

E
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 16:22
Let X be a quantity of full glass of wine and Y be a quantity of full bottle.

From the question....

9 * 3/4 X = 80 % Y

6.75 X = 80/100 Y

X>8 Y

So E.
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 19:57
D) 8 glasses

To fill 9 glasses with 3/4 wine each, we need 0.8 of a bottle.
To fill 1 glass, 0.8/(0.75*9)

To fill 75 such glasses, 80/9 bottles which are 80% full. If the bottles were 100% full, we will need only (80/9)*4/5 = 64/9 = 8 bottles.
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   08 Oct 2006, 22:31
The contents of bottle of wine that is 80% full can be emptied into 9 identical glasses so that each glass is ¾ full. How many identical, completely full bottles would be needed to completely fill 75 such glasses?

(A) 5 (B) 6 (C) 7 (D) 8 (E) more than 8

0.8 of a Bottle = 9 glasses (3/4 ofcourse)
08*B = 9
B = 45/4. So I full bottle will fill 45/4 glasses.

Now

3/4 fill 4 glasses = 3 (full glasses).
3/4 of 45/4 glasses = 3/4 * 45/4 = 135/16 completely filled glasses.

135/16 glasses are required to fill 1 Bottle

1 glass ------ 16/135 bottle
75 glasses ---- (16/135) * 75 = 400/27

a lot more than 8 glasses

OA is E.
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   09 Oct 2006, 01:46
kevincan wrote:
The contents of bottle of wine that is 80% full can be emptied into 9 identical glasses so that each glass is ¾ full. How many identical, completely full bottles would be needed to completely fill 75 such glasses?

(A) 5 (B) 6 (C) 7 (D) 8 (E) more than 8


0.8B=4/5B=9*(3/4)*G

Find 75G in terms of B:

(16/45)*B=3G (400/45)*B=75G=(80/9)*B

Since 8<80/9<9, 9 bottles are needed

OA=E
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Re: The contents of bottle of wine that is 80% full can be [#permalink] New post   09 Oct 2006, 08:30
[solution

ans=80/9..hence 9 bottles
choice E



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Re: The contents of bottle of wine that is 80% full can be [#permalink]
09 Oct 2006, 08:30
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