The theater sells two types of tickets: adult tickets for $15 and child tickets for $10. Last night, the theater sold a total of 336 tickets for a total of $4675. How many adult tickets did they sell?

Answer 1

Hi Tieisha,

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!

Answer 2

In order to solve this problem, we need a system of equations.

Let’s have x be equal to the number of adult tickets and y be equal to the number of child tickets.

We know that the total number of tickets is 336, so x+y=336.

We also know that the total cost of the tickets is $4675, and adult tickets are $15/tickets and child tickets are $10/ticket. Therefore $15*x+$10*y=$4675.

The complete system is:

x+y=336

15x+10y=4675

To solve this system of equations, we can use substitution. From the first equation, we can solve in terms of y to get x=336-y. By plugging that into our second equation, we can simplify to (15*336)-15y+10y=4675

5040-5y=4675

5y=365

y=73

Finally, we plug our answer for y into the first equation to get our answer for x.

x=336-73

x=263

Answer: There are 263 adult tickets and 73 child tickets.