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A dairy needs 357 gallons of milk containing 5% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 1% butterfat must be used to obtain the desired 357 gallons?

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sqdancefan

9514 1404 393

Answer:

  • 238 gallons 7%
  • 119 gallons 1%

Step-by-step explanation:

Let h represent the number of gallons of high butterfat content milk. Then 357-h will be the number of gallons of 1% milk. The total amount of butterfat in the mix is ...

  0.07h +0.01(357 -h) = 0.05(357)

  0.06h = 14.28 . . . . . . . . . . subtract 3.57, collect terms

  h = 238 . . . . . . . . . .  divide by 0.06

  357-h = 357 -238 = 119

238 gallons of 7% and 119 gallons of 1% are needed.

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