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grades of milk

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grades of milk

by lukaswelker » Tue Apr 08, 2014 10:08 am
Hey Guys, for this own I'm totally lost

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 1.5 percent grade, what is X in terms of Y and Z?

Y+3Z ; (Y+Z)/4 ; 2Y+3Z; 3Y+Z ; 3Y+4.5Z

How can one resolve this?
Many thanks
Lukas
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by Brent@GMATPrepNow » Tue Apr 08, 2014 10:11 am
Three grades of milk: 1%, 2%, and 3% fat by volume. X gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?
a. y + 3z
b. (y + z)/4
c. 2y + 3z
d. 3y + z
e. 3y + 4z
Let's start with a "word equation" and slowly turn it into an algebraic expression:

Total fat in mixture = 1.5% of (x+y+z)
(1% of x) + (2% of y) + (3% of z) = 0.015(x+y+z)
Rewrite as: 0.01x + 0.02y + 0.03z = 0.015x + 0.015y + 0.015z
Multiply both sides by 100: 1x + 2y + 3z = 1.5x + 1.5y + 1.5z
Rearrange and simplify: 0.5y + 1.5z = 0.5x
Multiply both sides by 2: y + 3z = x

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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