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A convenience store currently stocks 48 bottles of mineral

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Intern
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A convenience store currently stocks 48 bottles of mineral [#permalink] New post 27 Jun 2007, 16:26
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A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
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Director
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Re: PS: convenience store [#permalink] New post 27 Jun 2007, 16:55
dred wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
10
20
30
32
34


D.

20 p + 40 (1-p) = 35
p = 1/4
so 20 oz = 12

12 x 20 / (12+x) + 40x / (12+x) = 25

x = 4
so 32 bottles with 40 oz should be sold.
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Re: PS: convenience store [#permalink] New post 27 Jun 2007, 17:18
[
Thanks Himalayan.

Can you please explain how used this shortcut route of
20p + 40(1-p) = 35

I typically would have solved for x & y in the two equations
x + y = 48
and 20 x + 40 y / (x + y) = 35
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Senior Manager
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 [#permalink] New post 27 Jun 2007, 20:51
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Here is how I got it:

Average is 35 ounces
x is # of 20 ounce bottles
y is # of 40 ounce bottles

20x+40y/x+y = 35
solve to get y=3x

x+y=48 bottles
x=12, y=36

20x+40z/x+z=25

plug x=12 and solve for z, we get z = 4

So, y-z is # of bottles sold i.e 36-4 = 32
  [#permalink] 27 Jun 2007, 20:51
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