SOLUTION: A chemist mixes a 10% solution with a 50% acid solution to form 400ml of a 40% solution. How much of each solution should be used in the mixture?

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Question 820344: A chemist mixes a 10% solution with a 50% acid solution to form 400ml of a 40% solution. How much of each solution should be used in the mixture?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
u = volume of the 10% solution
v = volume of the 50% solution

%2810u%2B50v%29%2F%28400%29=40 and u%2Bv=400
Solve for u and v.

First simplify the rational equation:
10%28u%2B5v%29=16000
highlight_green%28u%2B5v=1600%29
Next, for convenience, subtract the "400" equation from this simplified "1600" equation and solve for v; and then use either equation to finish solving for the value of u.