Question 180957
Let x= amount of pure acid that is needed

Now we know that the amount of pure acid that is needed(x) plus the amount of pure acid in the 60% solution(0.60*40) has to equal the amount of pure acid in the final mixture(0.75(40+x)).  So our equation to solve is:

x+0.60*40=0.75(40+x)  get rid of parens and simplify
x+24=30+0.75x subtract 0.75x and also 24 from each side
x-0.75x+24-24=30-24+0.75x-0.75x  collect like terms
0.25x=6  divide each side by 0.25
x=24 gal-------------------------------amount of pure acid needed

CK
24+0.60*40=0.75*64
24+24=48
48=48

Hope this helps---ptaylor