1. Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1%, y gallonsof 2% and z gallons of 3% 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
c. 2y+3z
d. 3y+z
e. 3y+4.5z

please can u explain me the solution.

thanks

(.01x + .02y+.03z)/(x+y+z)=.015
=>x=y+3z

What is the official answer?

The answer is A (x=y+3z)

mixture problems work in the same way as RTD problems; the equation, in this case, is (% fat) x (total gallons) = (gallons of fat). the % works like a rate, the total gallons like a time, and the gallons of fat like a distance.

set up a chart, in which the rows are (% fat), (total gallons), and (gallons of fat).
first row: 0.01, x, 0.01x
second row: 0.02, y, 0.02y
third row: 0.03, z, 0.03z
TOTALS row: 0.015, (x + y + z), (0.01x + 0.02y + 0.03z) -- notice that both of the "gallons" columns add, but the percentages DON'T add.

therefore, 0.015(x + y + z) = 0.01x + 0.02y + 0.03z

the rest of the problem is as posted above.

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you can also pick numbers; i can show detail of this method if you like.

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gallons of fat! yummy!