A dairy needs 375 gallons of milk containing 5% butterfat. how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 375 gallons?

Suppose x amount of 7% and y amount of 2% be used to make 375 gallon of 5%.

Thus total amount will be:

x+y=375

⇒y=375-x ... i

also:

0.07x+0.02y = (375*0.05)

0.07x+0.02y=18.75 ... ii

substituting i in ii we get:

0.07x+0.02 (375-x) = 18.75

0.07x+7.5-0.02x=18.75

putting like terms together and simplifying we get:

0.05x=11.25

x=225 gallons

hence

y=375-225=150 gallons

thus

225 gallons of 7% and 150 gallons of 2% should be used.