SOLUTION: How many gallons of a 30% acid solution must be mixed with 30 gallons of a 17% solution to obtain a solution that is 20% acid. I've tried this problem a couple times, but cant

Question 163285: How many gallons of a 30% acid solution must be mixed with 30 gallons of a 17% solution to obtain a solution that is 20% acid.

I've tried this problem a couple times, but cant get the right answer. The answer was given to me by my teacher, but I need to show how to do the problem, which I can't. The answer to the problem is 9, i would appreciate it if you explained how to do the problem thoroughly.
Answer by Anthea Lawn(22) (Show Source): You can put this solution on YOUR website!
First of all, consider : How much pure acid is in 30 gallons of 17% acid ?
The answer is 17% of it : 17% X 30 = 0.17 X 30 = 5.1 gallons of pure acid
Now, start thinking about the 30% acid.
If you have N gallons of the stuff, how much of THAT is pure acid ?
The answer is 30% of N, or expressed algebraically, 0.3N.
If you mix the 30 gallons of 17% acid with N gallons of 30% acid, how many gallons of acid in total will there be ?
answer : 30 + N gallons in total
And of that, the amount which is pure acid is 5.1 (from above) + 0.3N.
The concentration of the mix is given by the number of gallons of pure acid divided by gallons of total acid,
which is :
(5.1 + 0.3N)/(30 + N)
Now we know that want the resulting concentration to by 20%, or, to put it another way, one fifth
(5.1 + 0.3N)/(30 + N) = 1/5
5(5.1 + 0.3N) = 30 + N
25.5 + 1.5N = 30 + N
4.5 = 0.5N
N = 9 (which was the answer you had)
Hope that helps !!

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