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# Three grades of milk are 1 percent, 2 percent, and 3 percent

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Joined: 21 Jul 2006
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Three grades of milk are 1 percent, 2 percent, and 3 percent [#permalink]  07 Dec 2007, 06:21
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Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent 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

Director
Joined: 12 Jul 2007
Posts: 865
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A. y + 3z

(x + 2y + 3z)/(x+y+z) = 1.5
x + 2y + 3z = 1.5x + 1.5y + 1.5z
.5x = .5y + 1.5z
x = y + 3z

Try it out by plugging 1 gallon into y and z

x = 1 + 3(1)
x = 4

so 4 gallons of 1%, 1 gallon of 2% and 1 gallon of 3%

Fat = (4*1) + 2 + 3 = 9
Milk = (4*1) + 1 + 1 = 6

9/6 = 1.5

it checks out
Director
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Re: PS: Percentages [#permalink]  07 Dec 2007, 06:59
tarek99 wrote:
Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent 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

1x+2y+3z = 1.5(x+y+z)

Then solve for x
1x+2y+3z = 1.5x+1.5y+1.5z
x=1.5x-.5y-1.5z
x=y+3z
Ans A
Re: PS: Percentages   [#permalink] 07 Dec 2007, 06:59
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