SOLUTION: Forty gallons of a 60% acid solution is obtained by mixing a 75% solution with a 50% solution. How many gallons of each solution must be used to obtain the desired mixture?

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Question 915702: Forty gallons of a 60% acid solution is obtained by mixing a 75% solution with a 50% solution. How many gallons of each solution must be used to obtain the desired mixture?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The method here makes sense only if the percents are volume per volume; otherwise, other details might be necessary.

u, volume of 50%
v, volume of 75%

%28acid%29%2F%28mixture%29=fraction
The fraction could be used as a percentage.
%2850u%2B75v%29%2F40=60

50u%2B75v=2400
10u%2B15v=480
2u%2B3v=96

u%2Bv=40, using just sum of the material volume quantities.

Linear system of equations, highlight_green%28system%282u%2B3v=96%2Cu%2Bv=40%29%29