dairy needs 357 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 4% butterfat must be used to obtain the desired 357 gallons?

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Define x and y :
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Let the amount of milk containing 7% butterfat be x gallons.
Let the amount of milk containing 4% butterfat be y gallons.

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Construct equations :
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Total milk needed = 357
x + y = 357

Percentage of butterfat needed = 6%
0.07x + 0.04y = 0.06 x 357
0.07x + 0.04y = 21.42

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Solve for x and y :
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x + y = 357         ---------------------- (1)
0.07x + 0.04y = 21.42  -------------- (2)


From Equation (1) :
x + y = 357
x = 357 - y ------------------ Sub into (2)

0.07(357 - y) + 0.04y = 21.42
24.99 - 0.07y + 0.04y = 21.42
24.99 - 0.03y = 21.42
0.03y = 24.99 - 21.42
0.03y = 3.75
y = 3.75 ÷ 0.03 = 125 ---- sub into (1)

x + y = 357
x + 125 = 357
x = 357 - 125
x = 232

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Find milk needed :
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amount of milk containing 7% butterfat = x = 232 gallons
 amount of milk containing 4% butterfat = y = 125 gallons.

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Answer: We need 232 gallons of the milk with 7% butterfat and 125 gallons of the milk with 4% butterfat to make the desire 357 gallons.
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