Dairy needs 357 gallons of milk containing 6% butterfat. how many gallons each of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain the desired 357 gallons?

Define x and y :

Let the amount of milk containing 7% butterfat be x gallons.
Let the amount of milk containing 4% butterfat be y gallons.


Construct equations :

Total milk needed = 357
x + y = 357

Percentage of butterfat needed = 6%
0.07x + 0.04y = 0.06 x 357
0.07x + 0.04y = 21.42


Solve for x and y :

x + y = 357          (1)
0.07x + 0.04y = 21.42  (2)

From Equation (1) :
x + y = 357
x = 357 - y Sub into (2)

0.07(357 - y) + 0.04y = 21.42
24.99 - 0.07y + 0.04y = 21.42
24.99 - 0.03y = 21.42
0.03y = 24.99 - 21.42
0.03y = 3.75
y = 3.75 ÷ 0.03 = 125 sub into (1)

x + y = 357
x + 125 = 357
x = 357 - 125
x = 232


Find milk needed :

amount of milk containing 7% butterfat = x = 232 gallons
 amount of milk containing 4% butterfat = y = 125 gallons.


We need 232 gallons of the milk with 7% butterfat and 125 gallons of the milk with 4% butterfat to make the desire 357 gallons.