Answer :
Let's use the variable "A" to represent the number of adult tickets and "S" to represent the number of senior tickets.
If each adult ticket is $11, each senior ticket is $10, and the total ticket sales were $4,286, we can write the following equation:
[tex]11A+10S=4286[/tex]Also, if the number of senior tickets sold was 24 less than twice the number of adult tickets, we can write the following equation:
[tex]S=2A-24[/tex]Using this value of S in the first equation, we have that:
[tex]\begin{gathered} 11A+10\cdot(2A-24)=4286 \\ 11A+20A-240=4286 \\ 31A=4286+240 \\ 31A=4526 \\ A=\frac{4526}{31}=146 \end{gathered}[/tex]Now, finding the value of S, we have:
[tex]S=2\cdot146-24=292-24=268[/tex]So the number of tickets sold is 146 adult tickets and 268 senior tickets.