A dairy needs 327 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 327 gallons?

**x = gallons of milk containing 7% butterfat**

327 - x = gallons of milk containing 3% butterfat{there are 327 total gallons}

327 - x = gallons of milk containing 3% butterfat

0.07x + 0.03(327 - x) = 0.06(327) {percentage fat x gallons equals total percentage fat x gallons}

0.07x + 9.81 - 0.03x = 19.62 {used distributive property and multiplied}

0.04x + 9.81 = 19.62 {combined like terms}

0.04x = 9.81 {subtracted 9.81 from each side}

x = 245.25 {divided each side by 0.04}

327 - x {gallons of 3% butterfat}

= 327 - 245.25 {substituted 245.25 in for x}

= 81.75 {subtracted}

**245.25 gallons of 7%**

and

**81.75 gallons of 3%**

__Check__245.25 + 81.75 = 327 total gallons

**Double Check**

0.07(245.25) + 0.03(81.75) = 0.06(327) {substituted gallons and percentages}

17.1675 + 2.4525 = 19.62

19.62 = 19.62

**Ask the House**