SOLUTION: A chemist needs 40 liters of 20% acid solution. She has containers of 10% solution and 40% solution. How many liters of each should she combine to get the needed solution?

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Question 703083: A chemist needs 40 liters of 20% acid solution. She has containers of 10% solution and 40% solution.
How many liters of each should she combine to get the needed solution?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Available concentrations of acid are Pl and Ph for percentage low and percentage high respectively. Pt is for percentage concentration target. All Pl, Ph, Pt are as the FRACTIONAL decimal form. Vl and Vh are for volume of the low concentration acid material and for volume of the high concentration acid material, respectively.

The resulting mixture of Vl plus Vh must be 40 liters and the concentration must be Pt=0.20. The proportion equation then is:
%28V%5Bl%5D%2AP%5Bl%5D%2BV%5Bh%5D%2AP%5Bh%5D%29%2F%28V%5Bl%5D%2BV%5Bh%5D%29=P%5Bt%5D
and since we need to find both volumes, we must include
V%5Bl%5D%2BV%5Bh%5D=40.

We have a system and need to solve it for V%5Bl%5D and V%5Bh%5D.

Further note: In this case, since the total volume is a given contant, the rational equation for target concentration can use V%5Bt%5D, our known target volume of acid mixture, and we have the general equation,
%28V%5Bl%5D%2AP%5Bl%5D%2BV%5Bh%5D%2AP%5Bh%5D%29%2FV%5Bt%5D=P%5Bt%5D