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

x=y+3z

Step-by-step explanation:

If we mixed the three grades of milk, the total percentage of fat by volume is given by:

(1%*x)+(2%*y)+(3%*z)

Where x is the number of gallons of 1% grade, y is the number of gallons of 2% grade and z is the number of gallons of 3%

We want that these percentage be equal to 1.5% of the total volume, so we create the following equation:

1.5%( x + y + z ) = (1%*x) + (2%*y )+ (3%*z)

Solving for x, we get:

1.5%*x + 1.5%*y + 1.5%*z = 1%*x + 2%*y + 3%*z

1.5%*x - 1%*x = 2%*y + 3%*z - 1.5%*y - 1.5%*z

0.5%*x = 0.5%*y + 1.5%*z

x = y + 3z

Then x in terms of y and z is x=y+3z

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step-by-step explanation:

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