SOLUTION: To be considered “nectar” a drink must contain 50% fruit juice. Find how much pure (100%) fruit juice and how much fruit drink (30%) must be mixed to make 7 gallons of “necta

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Question 1149985: To be considered “nectar” a drink must contain 50% fruit juice. Find how much pure (100%) fruit juice and how much fruit drink (30%) must be mixed to make 7 gallons of “nectar”.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
x of 30%
y of 100%

system%28x%2By=7%2C3x%2B10y=5%2A7%29
You want the value of x.

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


First, a standard algebraic approach....

You are mixing x gallons of 100% juice and (7-x) gallons of 30% juice to get 7 gallons of 50% juice:

1.00%28x%29%2B0.30%287-x%29+=+0.50%287%29

Solve using basic algebra.

Next, a completely different approach which is much faster and easier -- if you understand it....

(1) 50% is 2/7 of the way from 30% to 100% (picture the 3 percentages on a number line, if it helps....)
(2) Therefore, 2/7 of the mixture needs to be what you are adding.

ANSWER: The mixture needs to be 2/7 of the total 7 gallons, or 2 gallons, of the 100% juice, with the other 5 gallons the 30% juice.