Question

The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.

Answer 1

83 adult tickets and 217 student tickets.

Explanation:

Let number of adult tickets sold =
`x`

Given that total number of tickets = 300

So, number of student tickets = 300 -
`x`

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $
`15x`

Total collection from student tickets =
`(300-x)* 11 = 3300-11x`

Given that overall collection = $3630

`15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5`

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632