SOLUTION: How many gallons of a 40% solution must be mixed with 96 gallons of 60% solution to obtain a 52% solution?

Question 94760: How many gallons of a 40% solution must be mixed with 96 gallons of 60% solution to obtain a 52% solution?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of gal of 40% solution needed
Now we know that the amount of pure liquid in the 40% solution (0.40x) plus the amount of pure liquid in the 60% solution (0.60*96) has to equal the amount of pure liquid in the final mixture(96+x)*0.52. So our equation to solve is:
0.40x+(0.60*96)=0.52(96+x) get rid of parens
0.40x+57.6=49.92+0.52x subtract 0.52x and also 57.6 from both sides
0.40x-0.52x+57.6-57.6=49.92-57.6+0.52x-0.52x collect like terms
-0.12x=-7.68 divide both sides by -0.12
x=64-------------------------number of gal of 40% solution needed
CK
0.40*64+0.60*96=0.52(96+64)
25.6+57.6=83.2
83.2=83.2

Hope this helps------ptaylor

RELATED QUESTIONS
How many gallons of a 85% solution must be mixed with 96 gallons of 40% solution to... (answered by ankor@dixie-net.com)

How many gallons of 40 percent alcohol solution must be mixed with 70 percent solution to (answered by Grinnell)

How many gallons of 40 percent alcohol solution must be mixed with 70 percent solution to (answered by Alan3354)

how many gallons of 60% alcohol solution must be mixed with 60 gallons of 14% solution to (answered by josgarithmetic)

How many gallons of a 40 percent solution must be mixed with 60 gallons of a 22 percent... (answered by stanbon)

How many gallons of acid must be mixed with 40 gallons of 60% acid solution to get a 75%... (answered by ptaylor)

How many gallons of a 70% salt solution must be mixed with 60 gallons of a 18% solution... (answered by kev82)

How many gallons of a 60% alcohol solution must be mixed with 60 gallons of a 15%... (answered by robertb)

How many gallons of 32% solution must be mixed with 70 gallons of 47% solution to obtain... (answered by Nate)