SOLUTION: How much of a(n) 70 % orange juice drink must be mixed with 14 gallons of a 30 % orange juice drink to obtain a mixture that is 50 % orange juice?

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Question 1065127: How much of a(n) 70 % orange juice drink must be mixed with 14 gallons of a 30 % orange juice drink to obtain a mixture that is 50 % orange juice?
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
50% is the average --> equal amounts

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

We need to add X gallons of 70% drink.
So the amount of juice in the final mixture (14+X)(0.5) must match the amount of juice we started with (0.3*14), plus the amount of 70% to be added (0.7*X):
Therefore (14+X)(0.5) = (0.3)(14) + (0.7)X
14+X = (0.3)(28) + (1.4)X (multiplied by 2)
14+X = 8.4 + 1.4X
5.6 = 0.4X
X = 5.6/0.4 = 14
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Ans: Adding highlight%2814%29 gal of 70% drink will bring the original 14 gal 30% drink up to 50%
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Check: (14+14)(0.5) = 14 and
(14)(0.3) + (14)(0.7) = 4.2 + 9.8 = 14 (ok)