Total tickets sold

Question

The college sold 1200 tickets to a concert for a total of $11,200. They sold adult tickets for $15, children tickeets for $10 and student tickets for $8. They sold three times as many student ticktes as adult and children combined. How many of each ticket were sold?

Answer 1

A = No. adults; C = No. children's; S = No. student's tickets.

A + C + S = 1,200.

Also 15A + 10C + 8S = $11,200.

We are also told that S = 3(A + C) so S = 3A + 3C

Substituting in 1st eqn: A + C + 3A + 3C = 1200 → 4A + 4C = 1200

Substituting in 2nd eqn: 15A + 10C + 8(3A + 3C) → 15A + 10C + 24A + 24C → 39A + 34C = 11200

So we have a system of equations involving variables A and C: Using substitution method:

39A + 34C = 11200

4A + 4C = 1200. Divide by 4: A + C = 300, then A = 300 - C

39(300 - C) + 34C = 11200 → 11700 - 39C + 34C = 11200 →-5C = -500 → C = 100

A = 300 - 100 = 200

S = 1200 - A - C = 1200 - 200 - 100 = 900

Check: 15(200) + 10(100) + 8(900) = 3000 + 1000 + 7200 = $11,200

Answer 2

15A +10C + 8S = 11200

A+C+S =1200

S =3(A+C) = 3A+3C

use substituion, elimination or matrix algebra to get

S=900 student tickets

A=200 adult tickets

C=100 child tickets

900=3(200+100)

15(200)+10(100)+8(900) = 11200

200+100+900= 1200