How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid?

My teacher taught me a simple equation for these types of problems:

(percent of solution * amount of solution) + (percent of solution * amount of solution) = (percent of solution * total amount of solution)

in simple terms: %amount + %amount = %total amount

We know don't know how much gallons of 60% solution we need so it will be represented as x. We dont know the total amount either so it would have to be both solutions added together so 50 + x. Now lets solve:

(0.60) (x) + (0.24) (50) = (0.50) (50 + x) simplify / distribute

0.6x + 12 = 25 + 0.5x get all xs on one side and numbers on other

0.1x + 12 = 25

0.1x = 13 divide both sides by 0.1 to find x

x = 130

You need 130 gallons of 60% solution.