Three grades of Milk are 1%,2% and 3% fat by Vol. 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. (y+z)/4
e. 3y+z
We can plug in values.
It is MUCH easier to determine how to mix only TWO of the grades of milk than how to mix all three of the grades.
Thus, we should plug in 0 for one of the three grades of milk so that the mixture will be composed of only TWO of the grades of milk.
When equal amounts of two percentages are combined, the percentage in the mixture will be HALFWAY between the two percentages.
HALFWAY between two percentages is equal to the AVERAGE of the two percentages.
Thus, combining equal amounts of X (1% milkfat) and of Y (2% milkfat) will yield a mixture that is HALFWAY between 1% and 2%:
(1+2)/2 = 1.5% milkfat.
Let x=2, y=2 and z=0 (implying that no Z will be in the mixture).
The question asks for the value of x=2. This is our target.
Now we plug y=2 and z=0 into the answers to see which yields our target of 2.
Only answer choice
A works:
y+3z = 2 + 3*0 = 2.
The correct answer is
A.
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