SOLUTION: A dairy needs 310 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired

    x +     y = 310,        (1)    (milk volume balance, in liters)
0.07x + 0.02y = 0.06*310    (2)    (butterfat balance)

From (1), express y = 310 - x and substitute it into equation (2). You will get

0.07x + 0.02*(310 - x) = 18.6.

Simplify and solve for x:

0.07x + 6.2 - 0.02x = 18.6,

0.05x = 18.6 - 6.2,

0.05x = 12.4,

x =  = 248.

Answer. 248 liters of the 0.06% butterfat and 310-248 = 62 liters of the 0.02% butterfat.