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ratios - grades milk

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by Xbond » Mon Jun 01, 2009 1:05 pm
Hi there,

Could you help me to resolve this PS step by step. I'm lost.

Three grades of milk are 1%, 2%, 3% fat by volume. If x gallons of the 1% grade, y gallons of the 2% grade and z gallons of the 3% grade are mixed to give x+y+z gallons of a 1.5% grade, what is x in terms of y and Z ?

(A) y+3Z (B) (y+z)/4 (C) 2y+3z (D) 3y+z (E) 3y+4.5z

I thinks that the answser is A
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by SanjeevK » Mon Jun 01, 2009 1:18 pm
x gallon of 1% grade milk will have x/100 gallons of pure milk
y gallons of 2% grade milk will have 2y/100 gallons of pure milk
z gallons of 3% grade milk will have 3y/100 gallons of pure milk
(here by pure I mean 100% fat milk)

After mixing we get x+y+z gallons of 1.5% grade milk i.e 3(x+y+z)/200 gallons of pure milk

Equating the equations:
x/100 + 2y/100 + 3z/100 = 3(x+y+z)/200

Solving this we get x = (y+3z)
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by ManSab » Sun Jun 07, 2009 12:34 pm
SanjeevK,

Can you elaborate this please:
1.5% grade milk i.e 3(x+y+z)/200 gallons of pure milk

Thanks
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by SanjeevK » Sun Jun 07, 2009 5:19 pm
convert 1.5% to fraction. 1.5% = 1.5/100 = 3/200
Hope this helps
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by Xbond » Mon Jun 08, 2009 1:16 pm
Many thks
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