Question

A dairy needs 240 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 2% butterfat must be used to obtain the desired 240 gallons?

a) 120 gallons of 6% butterfat, 120 gallons of 2% butterfat
b) 160 gallons of 6% butterfat, 80 gallons of 2% butterfat
c) 80 gallons of 6% butterfat, 160 gallons of 2% butterfat
d) 200 gallons of 6% butterfat, 40 gallons of 2% butterfat

Answer 1

To obtain 240 gallons of milk containing 5% butterfat, 200 gallons of milk containing 6% butterfat and 40 gallons of milk containing 2% butterfat must be used. Therefore, the correct answer is d) 200 gallons of 6% butterfat and 40 gallons of 2% butterfat.

Step-by-step explanation:

To determine how many gallons of each type of milk must be used to obtain the desired 240 gallons of milk with a 5% butterfat content, let's set up a system of equations.

Let x represent the number of gallons of milk containing 6% butterfat and y represent the number of gallons of milk containing 2% butterfat.

We can set up the following equations:

x + y = 240 (equation 1)

0.06x + 0.02y = 0.05(240) (equation 2)

Multiplying equation 2 by 100 to remove the decimals gives us:

6x + 2y = 12 (equation 3)

Now we can solve the system of equations. Multiplying equation 1 by -6 gives us -6x - 6y = -144. Adding this equation to equation 3 eliminates x, and we are left with -4y = -132. Solving for y gives us y = 33.

Substituting y = 33 into equation 1 gives us x + 33 = 240. Solving for x gives us x = 207.

Therefore, the correct answer is d) 200 gallons of 6% butterfat and 40 gallons of 2% butterfat.