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A fruit punch that contains 10% fruit juice is combined with 100% fruit juice. How many ounces of each should be used to make 51oz of a mixture that is 70% fruit juice?

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Sqdancefanidn

9514 1404 393

Answer:

  • 34 oz 100%
  • 17 oz 10%

Step-by-step explanation:

Let j represent the number of ounces of 100% juice in the mix. Then (51-j) is the number of ounces of 10% juice. The total amount of fruit juice in the punch mix is ...

  1.00j + 0.10(51 -j) = 0.70(51)

  0.90j = 51(0.70 -0.10) . . . . . . . . collect j terms, subtract 0.10(51)

  j = 51(0.60/0.90) = 51(2/3) = 34 . . . . . . . divide by the coefficient of j

The mixture should use 34 ounces of 100% juice and 17 ounces of 10% juice.

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