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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 310 gallons?
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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.