Word problem involving ticket sales

If there were 32 people at a performance and the theater collected $474 from ticket sales, how many children attended the play? 

x = number of child tickets sold
32 - x = number of adult tickets sold {32 people attended}

12x + 17(32 - x) = 474 {price of ticket x number of tickets equals total value}
12x + 544 - 17x = 474 {used distributive property}
-5x + 544 = 474 {combined like terms}
-5x = -70 {subtracted 544 from each side}
x = 14 {divided each side by -5}

14 children attended

- Algebra House