20% solution added to 50% solution to get 30% solution

Hi can anyone help me with this problem, I am having a hard time setting it up. Thanks

How much of a 20% solution of alcohol and how much of a 50% solution should be mixed to give 8 gallons of a 30% solution?

let x = number of gallons of 20% solution
then 8 - x = number of gallons of 50% solution

(.20)x + .50(8 - x) = .30(8)

multiply every term by 100 to clear the decimals

20x + 50(8 - x) = 30(8)

solve for x ... then determine 8-x

thank you so much