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Three grades of milk are 1%, 2 % and 3% fat by volume. If x

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Three grades of milk are 1%, 2 % and 3% fat by volume. If x [#permalink] New post 02 Nov 2005, 13:19
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Three grades of milk are 1%, 2 % and 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 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
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 [#permalink] New post 02 Nov 2005, 13:29
1/100*x + 2/100*y + 3/100*z = (x+y+z)*1.5/100

get rid of 100

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

then multiply 2

2x + 4y + 6z = 3x + 3y + 3z

solve for x

x = y + 3z

A

Last edited by conocieur on 02 Nov 2005, 15:32, edited 2 times in total.
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 [#permalink] New post 02 Nov 2005, 13:31
hmm A?

lets say 1x+2y+3z=3/2(x+y+z)

bring all the X to one side...you get x=y+3z
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Re: PS # grades of milk [#permalink] New post 02 Nov 2005, 15:16
nakib77 wrote:
Three grades of milk are 1%, 2 % and 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 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


1% of x has .01x of fat, 2% has .02y of fat.. and .03 of fat..
total fat = .015..

.01x + .02y + .03z = .015
or.. x = 1.5-(2y+3z)

so.. x in terms of y and z is 2y + 3z.. constant can be ignored
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 [#permalink] New post 02 Nov 2005, 15:38
yup OA is A.
Thanks.
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  [#permalink] 02 Nov 2005, 15:38
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Three grades of milk are 1%, 2 % and 3% fat by volume. If x

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