Question

The theater sells two types of tickets: adult tickets for $13 and child

tickets for $2.
Last night, the theater sold a total of 212 tickets for a total of
$1942. How many adult tickets did the theater sell last night?

Answer 1

Let's first break apart the problem!

Let x = adult tickets

Let y = child tickets

We know from the problem that a total of 336 tickets were sold.

x + y = 336

We also know from the problem the total profit was $4675. We also know that the adult tickets were $15 per ticket and the child tickets were $10 per ticket.

15x + 10y = 4675

Now we need to combine our two-equation by making a common variable. Let's multiply our first equation by 10 and then combine the two equations.

10x + 10y = 3360

Now lets combine the equations

15x 10y = 4675

-10x - 10y = -3360

to get

5x = 1315

x = 263

Therefore there were 263 adult tickets sold.

I hope this helps