Question 132225
Well, congratulations for giving it a try!
Here's how to set it up:
Let x = the number gallons of 20% acid solution, as you did, so the amount of acid you would have is just 20% of x or 0.2x
Now you want to add (12-x) gallons of 50% acid solution (0.5(12-x) to make a total of 12 gallons of 30% acid solution (0.3(12)), so...
0.2x+0.5(12-x) = 0.3(12) Simplify and solve for x.
0.2x+6-0.5x = 3.6 Combine like-terms.
-0.3x+6 = 3.6 Subtract 6 from both sides.
-0.3x = -2.4 Finally, divide both sides by -0.3
x = 8 gallons of the 20% acid solution.
12-x = 12-8 = 4 gallons of the 50% acid solution.