SOLUTION: One brand of cleaner used to etch concrete is 20% acid. A stronger industrial strength cleaner is 40% acid. How many gallons of each cleaner should be mixed to produce 10 gallons o

Question 94774: One brand of cleaner used to etch concrete is 20% acid. A stronger industrial strength cleaner is 40% acid. How many gallons of each cleaner should be mixed to produce 10 gallons of 26% acid solution?

How do I do this problem, very confused. Thanks tutors.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=number of gal of 20% acid needed
Then 10-x=number of gal of 40% acid needed
Now we know that the amount of pure acid in the 20% solution (0.20x) plus the amount of pure acid in the 40% solution (0.40(10-x)) has to equal the amount of pure acid in the final mixture (0.26*10). So our equation to solve is:
0.20x+0.40(10-x)=0.26*10 get rid of parens
0.20x+4-0.40x=2.6 subtract 4 from both sides
0.20x+4-4-0.40x=2.6-4 collect like terms
-0.20x=-1.4 divide both sides by -0.20
x=7------------------------------number of gal of 20% solution needed
10-x=10-7=3--------------------number of gal of 40% solution needed
CK
7+0.20+3*0.40=10*0.26
1.4+1.2+2.6
2.6=2.6
Hope this helps--------------ptaylor
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