Question

The theater sells two types of tickets: adult

tickets for $14 and child tickets for $6.
Last night, the theater sold a total of 378
tickets for a total of $4252. How many adult
tickets did the theater sell last night?
a
a
Show your work here

Answer 1

Answer: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.

Answer 2

Let's set some variables:

• # of adult tickets: a
• # of child tickets: c

Now lets set up the system of equation:

.a + c = 378 --> 14a + 14c = 5292

14a + 6c = 4252

After solving the system of equation, you would get that

a = 248 and c = 130

That means the theater sold 240 adult tickets and 130 child tickets

Hope that helps!