Let:
x = Gallons of milk 7% fat
y = Gallons of milk 2% fat
The total gallons of milk needed is 375, thus:
x + y = 375 [Equation 1]
x gallons of milk add 0.07x fat to the mix and y gallons of milk add 0.02 fat to the mix. The total fat of the mix is:
0.07x + 0.02y
We know the total fat must be 5% of 375 gallons, that is:
0.05 x 575 = 18.75
Therefore, we get the equation:
0.07x + 0.02y = 18.75 [Equation 2]
Solving equaton 1 for x:
x = 375 - y
Substituting in equation 2:
0.07(375 - y) + 0.02y = 18.75
Operating:
26.25 - 0.07y + 0.02y = 18.75
Subtracting 26.25:
- 0.07y + 0.02y = 18.75 - 26.25
Operating:
-0.05y = -7.5
Dividing by -0.05:
y = 150
Calculating x = 375 - y
x = 375 - 150 = 225
Solution:
225 gallons of milk containing 7% butterfat
150 gallons of milk containing 2% butterfat