grandh01 wrote:Three grades of milk are 1%, 2%, 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 a 1.5% grade, what is x in terms of y and z?
1) y + 3z
2) (y + z)/4
3) 2y + 3z
4) 3y + z
5) 3y + 4.5z
Thanks in advance
1.5% is halfway between 1% (the percentage in X) and 2% (the percentage in Y).
Thus, if we mix equal amounts of X and Y, the resulting mixture will be 1.5% fat.
To illustrate:
If X=100, Y=100, and Z=0, then fat/total = (1+2)/(100+100+0) = 3/200 = (1.5)/100 = 1.5%.
Let X=100, Y=100 and Z=0.
The question asks for the value of X=100. This is our target.
Now we plug Y=100 and Z=0 into the answers to see which yields our target of 100.
Only answer choice
A works:
y + 3z = 100 + 3*0 = 100.
The correct answer is
A.
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