Answer:
The cost of one adult ticket is $6 and the cost of one student ticket is $8.
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.
[tex]7a+13s=146[/tex]They sell $276 worth of tickets by selling 14 adult tickets and 24 student tickets.
[tex]\implies14a+24s=276[/tex]Thus, the system of equations to model the scenario is:
[tex]\begin{gathered} 7a+13s=146 \\ 14a+24s=276 \end{gathered}[/tex]Multiply the first equation by 2 and the second by 1.
[tex]\begin{gathered} 14a+26s=292 \\ 14a+24s=276 \end{gathered}[/tex]Subtract:
[tex]\begin{gathered} 2s=16 \\ s=\frac{16}{2} \\ s=8 \end{gathered}[/tex]Next, we solve for 'a' using any of the equations.
[tex]\begin{gathered} 7a+13s=146 \\ 7a+13(8)=146 \\ 7a+104=146 \\ 7a=146-104 \\ 7a=42 \\ a=\frac{42}{7} \\ a=6 \end{gathered}[/tex]Therefore, the cost of one adult ticket is $6 and the cost of one student ticket is $8.
Check
[tex]\begin{gathered} 7a+13s=146 \\ 7(6)+13(8)=146 \\ 42+104=146 \\ 146=146 \end{gathered}[/tex]