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 {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%Check245.25 + 81.75 = 327 total gallons Double Check0.07(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
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