paresh_patil 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
An alternate approach:
The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.
Let x=100, y=100, and z=0.
The resulting mixture will be 1.5% grade:
Fat/total = [.1(100) + .2(100) + .3(0)] / (100+100+0) = 3/200 = 1.5/100 = 1.5%.
The question asks for the value of x=100. This is our target.
Now plug y=100 and z=0 into the answers to see which yields our target of 100.
Only
A works:
y + 3z = 100 + 3(0) = 100.
The correct answer is
A.
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