A dairy needs 392 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 2% butterfat must be used to obtain the desired 392 gallons?

{x*0.02+0.06y=392*0.05

{x+y=392, x=392-y

0.04y=11.76, y=294; x=392-294=98

There is need 98 gallons of milk with 2% butterfat and 294 gallons of milk with 6% butterfat

Qty % Qty * %

Solution 1: x 6% = 0.06 = 0.06x

Solution 2: 392 - x 2% = 0.02 = 0.02 (392 - x) = 7.84 - 0.02x

Mixture: 392 5% = 0.05 = 0.06x + 7.84 - 0.02x

392 (0.05) = 0.08x + 7.84

19.6 = 0.08x + 7.84

11.76 = 0.08x

147 = x

Solution 2: 392 - x = 392 - (147) = 245

Answer: 147 gallons 6% and 245 gallons of 2%