SOLUTION: how many gallons of pure (100%) acid should be added to 5 gallons of a 40% acid solution to obtain a 50% acid solution?

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Question 170150: how many gallons of pure (100%) acid should be added to 5 gallons of a 40% acid solution to obtain a 50% acid solution?
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=gallons of pure acid

(100%)(x)+(40%)(5)=(50%)(x+5)

x+2=.5x+2.5

.5x=.5

x=1

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of gallons of pure (100%) acid to be added to 5 gallons of 40% acid solution. The end result will be 5+x gallons of 50% acid solution.
x + 0.4(5) = 0.5(5+x) Simplify.
x+2 = 2.5+0.5x Subtract 0.5x from both sides.
0.5x+2 = 2.5 Subtract 2 from both sides.
0.5x = 0.5 Divide both sides by 0.5
x = 1
You will need to add 1 gallon of pure (100%) acid to the 5 gallons of 40% acid solution to obtain 6 gallons of 50% acid solution.