Question

A dairy needs 225 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 225 gallons?

a) 125 gallons of 6% butterfat milk and 100 gallons of 1% butterfat milk
b) 100 gallons of 6% butterfat milk and 125 gallons of 1% butterfat milk
c) 150 gallons of 6% butterfat milk and 75 gallons of 1% butterfat milk
d) 75 gallons of 6% butterfat milk and 150 gallons of 1% butterfat milk

Answer 1

To obtain 225 gallons of milk with 5% butterfat, you would need 150 gallons of 6% butterfat milk and 75 gallons of 1% butterfat milk.

Step-by-step explanation:

To obtain 225 gallons of milk with 5% butterfat, we need to determine the number of gallons of milk with 6% butterfat and 1% butterfat that should be used. Let's assume x gallons of milk with 6% butterfat and y gallons of milk with 1% butterfat. The total gallons of milk equation can be set up as follows:

x + y = 225

The butterfat equation can be set up as:

0.06x + 0.01y = 0.05 * 225

Simplifying these equations, we get:

x + y = 225

0.06x + 0.01y = 11.25

Multiplying the second equation by 100 to eliminate decimals, we get:

6x + y = 1125

Now we can use the method of substitution or elimination to solve for x and y. The correct answer is option c) 150 gallons of 6% butterfat milk and 75 gallons of 1% butterfat milk.