SOLUTION: How much of Brand A fruit punch (40% fruit juice) must be mixed with 2 L of grape juice to create a mixture containing 64% fruit juice?

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Question 1157201: How much of Brand A fruit punch (40% fruit juice) must be mixed with 2 L of
grape juice to create a mixture containing 64% fruit juice?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
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Here is a non-standard, non-algebraic method for solving any two-part mixture problem like this.

You are starting with 2L of 100% grape juice; you are adding some 40% fruit juice to get a mixture that is 64% fruit juice.

Imagine the three percentages on a number line: 100, 64, and 40. Imagine "walking" along the number line, starting from 100 and moving toward 40, stopping when you get to 64. What fraction of the distance have you gone?

100 to 40 is 60; 100 to 64 is 36. You have gone 36/60 = 3/5 of the distance.

That means 3/5 of the mixture has to be the 40% fruit juice that you are adding to the original 100% grape juice.

So 2/5 of the mixture is the original 2L of grape juice; that means the 3/5 of the mixture is 3L.

ANSWER:
Add 3L of fruit juice to get a mixture that is 64% fruit juice.

CHECK:
1.00(2)+.40(3) = 2+1.2 = 3.2
.64(2+3) = .64(5) = 3.2