Question in description

Question

There were 600 people watching a play in a theatre. The number of adults was three times the number of children. The total amount collected from the sale of tickets for the play was $16800. The price of an adult ticket was twice the price of a child ticket. Find the total amount collected from the sale of the children's ticket.

Answer 1

A = number of adults

C = number of children

A + C = 600

A = 3C

 

3C + C = 600 ⇒ C = 600/4 = 150

 

p = price of child ticket 

2p = price of adult ticket

 

A(2p) + Cp = $16800

(3C)(2p) + Cp = 16800

 

We want to find Cp.

 

(3C)(2p) + Cp = 16800

7(Cp) = 16800

Cp = 16800/7 = 2400

 

The total amount collected from the sale of the children's tickets was $2400.

 

p = $2400/150 = $16

 

 

 

Test the solution.

Answer 2

let x = the number of children

3x = the number of adults

 

x + 3x = 600

4x = 600

x = 150

 

There were 150 children and 450 adults at the play

 

Now, let y = the price of a child's ticket

2y = the price of an adult ticket

 

150y + 450(2y) = 16800

150y + 900y = 16800

1050y = 16800

y = 16

 

Children's tickets were $16 each and adult tickets cost $32 each. The total collected from the sale of children's tickets is 150 * 16 = $2400.