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How much of an 80% orange juice drink must be mixed with 12 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice

Sagot :

sqdancefan

Answer:

  12 gallons

Step-by-step explanation:

The amount of juice in the mix is the sum of the amounts of juice contributed by each of the constituents of the mix. Those amounts will be the product of the quantity of constituent and the fraction that is juice.

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setup

Let x represent the amount of 80% juice drink that must be added to the mix. The total amount of orange juice in the mix is ...

  20% × 12 gallons + 80% × x gallons = 50% × (12 +x) gallons

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solution

Dividing by gallons, eliminating parentheses, and using decimals for percentages, we have ...

  2.4 +0.80x = 6.0 +0.50x

  0.30x = 3.6 . . . . . . . . subtract 0.50x+2.4

  x = 12 . . . . . . . . . . . divide by 0.30

12 gallons of 80% juice drink must be added to obtain the desired mix.

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Additional comment

We notice that 50% is the average of 20% and 80%, so each must be half of the mix. If there are 12 gallons of 20%, then there must be 12 gallons of 80%.

You can read more about mixture problems here:

https://brainly.com/question/26751698

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