Question

The school that Tyson attends is selling tickets to a performance. On the first day ofticket sales the school sold 5 adult tickets and 2 child tickets for a total of $138.50. The school tookin $185.50 on the second day by selling 7 adult tickets and 2 child tickets. Find the price of an adultticket and the price of a child ticket.

Answer 1

Let a represent the cost of adult tickets and c represent the cost of children's tickets.

On the first day, $138.50 worth of tickets were sold by selling 5 adult tickets and 2 child tickets. This means that:

`5a+2c=138.50`

On the second day, $185.50 worth of tickets were sold by selling 7 adult tickets and 2 child tickets. This means that:

`7a+2c=185.50`

We can solve the simultaneous equations by subtracting the two equations:

`\begin{gathered} 7a-5a+2c-2c=185.50-138.50 \\ 2a=47 \\ a=(47)/(2) \\ a=23.5 \end{gathered}`

We can solve for c by substituting for a into the first equation:

`\begin{gathered} 5(23.5)+2c=138.50 \\ 117.5+2c=138.50 \\ 2c=138.50-117.50=21 \\ c=(21)/(2) \\ c=10.5 \end{gathered}`

Therefore, an adult ticket costs $23.50 and a child ticket costs $10.50.