How much 30% paint thinner solution should be added to a gallon of 10% paint thinner solution to make a solution that is 20% paint thinner

1 gallon

Explanation:

You can set an equation in this way:

1) Number of gallons of 30% thinner solution to be added: x gallons

2) Amount of thineer in the x gallons: 0.30x

3) Amount of thineer in the 1 gallon solution of 10% thinner: 0.10 (1) = 0.10

4) Number of gallons of the final solution, which is 20%: 1 + x

5) Amount of thineer in the final 20% solution: 0.2 (1 + x)

6) Equality:

Amount of thinner in the 30% solution + amount of thinner in the 10% solution = amount of thinner in the 20% solution

0.30x + 0.1 = 0.2 (1 + x)

7) Solve

0.3x - 0.2x = 0.2 - 0.1

0.1x = 0.1

x = 1

That is 1 gallon of 30% thinner solution should be added.