Question

A theater has tickets priced at $6 for adults, $3.50 for students, and $2.50 for seniors. A total of 278 tickets were sold for one showing with a total revenue of 1300. If the number of adult tickets sold was 10 less than twice the numbers of student tickets, how many of each type of ticket were sold?

Answer 1

150 adult tickets, 80 student ticket and 48 senior tickets.

Explanation:

Given:

A theater has tickets priced at $6 for adults, $3.50 for students, and $2.50 for seniors.

A total of 278 tickets were sold for one showing with a total revenue of 1300.

If the number of adult tickets sold was 10 less than twice the numbers of student tickets.

Question asked:

How many of each type of ticket were sold?

Solution:

Let the number of students tickets sold =
`x`

Then the number of adult tickets sold =
`2x-10`

Then the number of senior tickets sold =

`278-(x+2x-10)=278-(3x-10)=278-3x+10=288-3x`

Total revenue = $1300

`3.5* x+6(2x-10)+2.5(288-3x)=1300\\ \\ 3.5x+12x-60+720-7.5x=1300\\ \\ 8x+660=1300\\ \\ Subtracting\ both\ sides\ by\ 660\\ \\ 8x=640\\ \\ Dividing\ both\ sides\ by\ 8\\ \\ x=80`

The number of students tickets sold =
`x` = 80

The number of adult tickets sold =
`2x-10` =
`2*80-10=160-10=150`

The number of senior tickets sold =
`288-3x=288-3*80=288-240=48`

Therefore, 150 adult tickets, 80 student ticket and 48 senior tickets are sold.