2000 tickets were sold for a play generating 19,700. The prices of the tickets were $5 for children, $10 for students and $12 for adults. There were 100 more adult tickets sold than students. Find the number of each type ticket sold.

Question

Find the number of each type sold.

Thanks for your help.

Answer 1

student tickets ---- x
adult tickets ------- x+100
children tickets ---- 2000 -x - (x+100) = 1900-2x

5(1900-2x) + 10x + 12(x+100) = 19700
9500 - 10x + 10x + 12x + 1200 = 19700
12x = 9000
x = 750 student tickets
x+100 = 850 adult tickets
leaving 400 children tickets

check:
5(400) + 10(750) + 12(850) = 19700