Question

The ticket sales at a movie theater were $4,286. Adult tickets are $11, and senior tickets are $10. The numbe of senior tickets sold was 24 less than twice the number of adult tickets. Determine the number of adult tickets and senior tickets sold.

Answer 1

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:

`11A+10S=4286`

Also, if the number of senior tickets sold was 24 less than twice the number of adult tickets, we can write the following equation:

`S=2A-24`

Using this value of S in the first equation, we have that:

`\begin{gathered} 11A+10\cdot(2A-24)=4286 \\ 11A+20A-240=4286 \\ 31A=4286+240 \\ 31A=4526 \\ A=(4526)/(31)=146 \end{gathered}`

Now, finding the value of S, we have:

`S=2\cdot146-24=292-24=268`

So the number of tickets sold is 146 adult tickets and 268 senior tickets.