Question

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 ?

A, y+3z
B, (y+z)/4
C, 2y+3z
D, 3y+z
E, 3y+4.5z

Answer 1

A is correct.

x = y + 3z.

Explanation:

Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume.

If x gallons of the 1 percent grade, 1% of x = 0.01x

If y gallons of the 2 percent grade, 2% of y = 0.02y

If z gallons of the 3 percent grade, 3% of z = 0.03z

Total number of gallons = x+y+z

Total grade = 1.5% of (x+y+z)

The amount of grade before and after mixing should be same.

According to question,

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

0.01x + 0.02y + 0.03z = 0.015x + 0.015y + 0.015z

0.015x - 0.010x = 0.020y - 0.015y + 0.030z - 0.015z

0.005x = 0.005y + 0.015z

x = y + 3z

Hence, The required equation will be x = y + 3z