Question

"It costs $12 for a ticket to a school play if you buy the ticket in advance. If you buy a ticket at the door, it will cost $15. The school made $3213 and 36 more tickets were sold in advance than at the door. How many tickets were sold in advance?"

I don't know how to write the equation to solve this word problem.

Answer 1

`139` tickets were sold in advance.

Explanation:

Let x be the number of tickets that were sold in advance.
`12x + 15(x-36) = 3213`
`12x + 15x - 540 = 3213`
`27x = 3753`
`x = 3753/27`
`x = 139`

Answer 2

There were `color(blue)(139` people who bought the tickets in advance and `color(blue)(103` who bought it at the door.

Explanation:

Let assume the number of people who bought the tickets at the door to be `color(red)(x-36`.

Number of people who bought the tickets in advance`color(red)(=x`.

`therefore` Total cost `color(darkorange)(=$12(x)+$15(x-36)`.

`$3213=$12(x)+$15(x-36)`

`$3213=12x+15x-540`

`$3213=27x-540`

`3213+540=27x`

`27x=3753`

`x=3753/27`

`color(magenta)(x=139`

Now, let us find the number of people who bought the ticket at the door`=x-36`.

`color(magenta)(139-36=103`

`therefore` There were `color(blue)(139` people who bought the tickets in advance and `color(blue)(103` who bought it at the door.

~Hope this helps! :)