Question

Two baseball teams have a game Monday night. Within the first minute, they sell 7 adult tickets and 13 student tickets for a total of $146. The next minute they sell $276 worth of tickets by selling 14 adult tickets and 24 student tickets. Create a system of equations to model the scenario. Determine the cost of one adult ticket and one student ticket. Use mathematics to justify your answer.

Answer 1

The cost of one adult ticket is $6 and the cost of one student ticket is $8.

Step-by-step explanation:

Let the cost of one adult ticket=a

Let the cost of one student ticket=s

They sell 7 adult tickets and 13 student tickets for a total of $146.

`7a+13s=146`

They sell $276 worth of tickets by selling 14 adult tickets and 24 student tickets.

`\implies14a+24s=276`

Thus, the system of equations to model the scenario is:

`\begin{gathered} 7a+13s=146 \\ 14a+24s=276 \end{gathered}`

Multiply the first equation by 2 and the second by 1.

`\begin{gathered} 14a+26s=292 \\ 14a+24s=276 \end{gathered}`

Subtract:

`\begin{gathered} 2s=16 \\ s=(16)/(2) \\ s=8 \end{gathered}`

Next, we solve for 'a' using any of the equations.

`\begin{gathered} 7a+13s=146 \\ 7a+13(8)=146 \\ 7a+104=146 \\ 7a=146-104 \\ 7a=42 \\ a=(42)/(7) \\ a=6 \end{gathered}`

Therefore, the cost of one adult ticket is $6 and the cost of one student ticket is $8.

Check

`\begin{gathered} 7a+13s=146 \\ 7(6)+13(8)=146 \\ 42+104=146 \\ 146=146 \end{gathered}`