Question

The school that Jack goes to is selling tickets to a play. On the first day of ticket sales the school

sold 10 senior citizen tickets and 5 child tickets for a total of $205.55. The school took in
$241.61 on the second day by selling 4 senior citizen tickets and 13 child tickets. What is the
price each of one senior citizen ticket and one child ticket?

Answer 1

The price of each senior citizen ticket is $13.31 and that of each child ticket is $14.49.

Explanation:

If the cost per single senior citizen ticket is x and the cost per single child ticket is y.

Now, 10 senior citizen tickets and 5 child tickets cost a total of $205.55.

Hence, 10x + 5y = 205.55 ....... (1)

⇒ 20x + 10y = 411.1 ....... (2)

And 4 senior citizen tickets and 13 child tickets for a total of $241.61.

Hence, 4x + 13y = 241.61 ........ (3)

⇒ 20x + 65y = 1208.05 ......... (4)

So, from equations (2) and (4) we get,

55y = 796.95

⇒ y = 14.49

And, from equation (1), we get

10x + 5(14.49) = 205.55

⇒ 10x = 133.1

⇒ x = 13.31

Therefore, the price of each senior citizen ticket is $13.31 and that of each child ticket is $14.49. (Answer)