SOLUTION: how much pure acid is in 800 gallons of a 38% acid soloution

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Question 252487: how much pure acid is in 800 gallons of a 38% acid soloution
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
38% of 800 is .38*800
38 is 2 less than 40
40% is .4=4/10
4/10*800=320
so 38% should be a little less than 320
2/100*800=16
320-16=304
304 gallons of acid in 800 gallons of 38%

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
how much pure acid is in 800 gallons of a 38% acid solution. We are obviously looking at a mixture problem.
Pure acid = 100%.
PURE . . . 100 . . . X . . . . . 100X
(B?) . . . ?? . . .. 800-X . . . 800? - x?
MIX . . . 38 . . . . 800 . . . . 30400
100X - ?X + 800? = 30400.
X = (30400 - 800?) / (100-?)
What we have here is a Diophantine equation. We are thinking what values of ? make X a nice integer?
If ? = 0, X = 304.
If ? = 20, X = 180.
If ? = 36, X = 25 .
Not sure which way you want to go on this.