Mixture of fatty milks

Anju@Gurome wrote:

actofman 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?

The concentration of milk in the mixture = 1% of x + 2% of y + 3% of z = (x + 2y + 3z)/100
Also, the concentration of milk in the mixture = 1.5% of (x + y + z) = (1.5)*(x + y + z)/100

So, x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5y + 1.5z = 0.5x
--> y + 3z = x

3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z

GMATGuruNY wrote:

3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z

The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.

Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.

The correct answer is A.

actofman wrote:

GMATGuruNY wrote:

3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z

The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.

Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.

The correct answer is A.

Thanks Mitch!

In your first paragraph, why was Z ignored? Only bec 1.5 is average of x and y values? So if 1% was y and 2% was Z, we'll ignore x bec y and z average to 1.5%?

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