SOLUTION: Ms. Lopez needs to make 70 millimeters of a 25% acid solution by mixing together a 15% acid solution with a 40% acid solution. How much of each solution must she use?

Question 478270: Ms. Lopez needs to make 70 millimeters of a 25% acid solution by mixing together a 15% acid solution with a 40% acid solution. How much of each solution must she use?
Found 2 solutions by stanbon, cleomenius:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Ms. Lopez needs to make 70 millimeters of a 25% acid solution by mixing together a 15% acid solution with a 40% acid solution. How much of each solution must she use?
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Equation:
acid + acid = acid
0.15x + 0.40(70-x) = 0.25*70
---
Multiply thru by 100 to get:
15x + 40*70 - 40x = 25*70
-25x = -15*70
x = (3/5)70
x = 42ml (amt. of 15% solution needed)
70-x = 28 ml (amt. of 40% solution needed)
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Cheers,
Stan H.
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Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
I would set up an allegation as follows:
Set up a tic tac toe board with:
40%, the highest concentration in the top left Square.
15%, the lowest concentration, in the bottom left Square.
25%, the percent we want in the middle Square.
40% | . . . | ... .
__________
. .. . | 25% | .. .
__________
15% | ... . | ... .
In the lower right corner, put 40% minus 25%; this is the parts of the 15 % you need.
In the upper right corner, put 25% minus 15%; this is the parts of the 40 % you need.
40% | . . . | 10
__________
. .. . | 25% | .. .
__________
15% | ... . | 15
The total parts you need is 25.
The 40% needs 10/25, or 2/5 of 70 ml = 28 ml.
the 15% needs 15/25, or 3/5 of 70 ml = 42 ml.

Cleomenius.

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