SOLUTION: 1.Jill combines 10% fruit juice with PURE fruit juice to make 2 liters of 25% fruit juice. How much pure fruit juice does she use in the mix? NOTE:( can you please show the wo

Question 286499: 1.Jill combines 10% fruit juice with PURE fruit juice to make 2 liters of 25% fruit juice. How much pure fruit juice does she use in the mix?

NOTE:( can you please show the work or somehow explain them so i can understand how to do it..thank you)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.Jill combines 10% fruit juice with PURE fruit juice to make 2 liters of 25% fruit juice. How much pure fruit juice does she use in the mix?
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Equation:
Solution using 2 variable:
Let x be amount of 10% juice
Let y = amount of 100% juice
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Quantity Equation: x + y = 2 liters
Pure juice Equations: 0.10x + 1.00y = 0.25*2
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Multiply thru 1st equation by 10
Multiply thru 2nd equation by 100
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10x + 10y = 20
10x + 100y = 25*2
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Subtract 1st equation from 2nd and solve for "y":
90y = 30
y = 1/3 liter (amount of pure fruit juice needed for the mixture)
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Solution using 1 variable:
Let x be amount of 10% juice.
Then 2-x is amount of 100% juice
pure + pure = pure
0.10x + 1(2-x) = 0.25*2
Multiply thru by 100 to get:
10x + 100(2-x) = 25*2
10x + 200-100x = 50
-90x = -150
x = 15/9
x = 5/3 liter
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2-(5/3) = 1/3 liter (amount of pure fruit juice needed for the mixture)
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Cheers,
Stan H.
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