Question

A dairy needs 365 gallons of milk containing 7% butterfat. How many gallons each of milk containing 9% butterfat and milk containing 4% butterfat must be used to obtain the desired 365 gallons?

Answer 1

The amount in gallons of each milk containing 9% butterfat and milk containing 4% butterfat which must be used to obtain the desired 365 gallons are;

• 219 gallons of 9% fat.
• 146 gallons of 7% fat.

What quantity of each type of milk is required for the desired 365 gallon?

It follows from the task content that the quantity of each type of milk required to arrive at the targeted fat content and quantity of milk are to be determined.

Let x = quantity of 9% fat milk and

Let y = quantity of 4% fat milk

Therefore, by mass balance; we have;

x + y = 365.

Where; y = 365 - x.

Also, by fat balance; we have;

(9% × x) + (4% × y) = (7% × 365)

9x + 4y = 2555

Therefore, the two equations to be solved simultaneously by substituting y from the first equation into the second equation as follows;

9x + 4 (365 - x) = 2555

5x = 1095

x = 1095/5

x = 219 gallons.

Also, y = 365 - 219 = 146 gallons.

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