A dairy needs 235 gallons of milk containing 4% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 285 gallons?8 & 3%?

Question

Homework question? 6 and 1% contained?

Answer 1

Convert all of your %'s into decimals by dividing by 100.

The total amount of butterfat needed is 0.04 times 235 or 9.4 gallons of butterfat

Let X be the number of gallons of the 6% butterfat milk.

Then 235 - X is the gallons of 1% butterfat milk used.

Then 0.06 times X + 0.01 times( 235 - X) = 9.4

Multiply through: 0.06 X + 2.35 - 0.01 X = 9.4

Combine terms: 0.05 x + 2.35 = 9.4

Subtract 2.35 from both sides: 0.05X = 7.05

Divide by 0.05: X = 141

Thus 141 gallons of 6% and 235 - 141 or 94 gallons of 1%.

For 3% the calculations are likewise as the total butterfat = 235 times 0.03 = 7.05 gallons of butterfat.

Use the same equation and logic as above with 7.05 replacing 9.4.

Then 0.06 times X + 0.01 times( 235 - X) = 7.05

Multiply through: 0.06 X + 2.35 - 0.01 X = 7.05

Subtract 2.35 from both sides: 0.05X = 4.7

Divide by 0.05: X = 94

Thus 94 gallons of 6% and 235 - 94 or 141 gallons of 1%.