SOLUTION: hey, this makes two solutions.one is 24 percent acid the rest is water and the other is 41 percent acid is about how much of each solution does she need to do 50 gallons of a solut

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Question 771326: hey, this makes two solutions.one is 24 percent acid the rest is water and the other is 41 percent acid is about how much of each solution does she need to do 50 gallons of a solution that is 31 percent 250 gallons of the solution that is 31 percent acid






Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Your question is confusing. Are you asking two questions?
Given information: 24% acid solution and 41% acid solution.
Wanted maybe: 50 gallons of 31% solution; and 250 gallons of 31% acid solution.

Let V = volume in gallons of the resulting solution when the two different concentrations are mixed.
Let x = volume of the 24% acid
let y = volume of the 41% acid

The initial untreated system: %2824x%2B41y%29%2FV=31 and x%2By=V

Dealing with the rational equation,
24x%2B41y=31V
So the system you can use to solve for x and y could be
highlight%2824x%2B41y=31V%29 and highlight%28x%2By=V%29


Pushing a little further, use the volume sum as 24x+24y=24V since this will allow elimination of the x terms:
24x%2B41y-%2824x%2B24y%29=31V-24V
41y-24y=7V
17y=7V
highlight%28y=7V%2F17%29
Substitute this into the volume sum to find x:
x=V-y
x=V-%287V%2F17%29
x=%2817-7V%29%2F17
highlight%28x=10V%2F17%29