SOLUTION: How many quarts of pure sulphuric acid should be added to 5 quarts of water to obtain a 40% solution?

Question 103139: How many quarts of pure sulphuric acid should be added to 5 quarts of water to obtain a 40% solution?
Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!
Let x=the amt. of sulfuric acid to be added
NOTE: Total amount(in quarts)*percentage of sulfuric acid(in %)=amount of sulfuric acid(in quarts)
Also, water does NOT CONTAIN any sulfuric acid so it is ZERO PERCENT acid! Consequently, if the sulfuric acid is defined to be PURE, it is ONE HUNDRED PERCENT acid!
For the original substance,
5*0=0
For the acid for addition,
x*100=100x
and, since it is mixture, the amounts must be added so the amount of the mixture is x+5 quarts! And as defined from the problem, the mixture would be 40 percent acid!
So,for the mixture,
40*(x+5)=40x+200
Furthermore, the amount of acid is equal to the sum of the amounts of acid of the previous substances, the water and the pure acid.
Thus,
100x+0=40x+200
60x=200
6x=20
x=20/6 or 10/3

Therefore, 10/3 or 3 1/3 quarts must be added to the 5 quarts of water to produce a solution with 40% sulfuric acid!

Please do not hesitate to ask if you need further assistance. Just call my name, HyperBrain!
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