Percentage Word Problem

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?

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x = gallons of milk containing 7% butterfat
327 - x = gallons of milk containing 3% butterfat   {there are 327 total gallons}

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

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