A theatre contains 468 seats and the ticket prices for a recent play...

Question

A theatre contains 468 seats and the ticket prices for a recent play were $42 for adults and $27 for children. If the total proceeds were $15,621 for a sold-out matinee, how many of each type of ticket were sold?

Answer 1

Total number of seats = 468

Since the show was sold out, tickets = seats = 468

Let's say:
number of adult tickets sold = a

number of child tickets sold = c

So, a + c = 468 

 

Now, let's look at the proceeds:

total proceeds = 15,621
proceeds from adult tickets = 42a
proceeds from child tickets = 27c
So, 42a + 27c = 15,621

This gives you two equations:

a + c = 468            (1)

42a + 27c = 15621 (2)

Rewrite (1), a + c = 468, as a = 468 - c

Now, replace a in (2), 42a + 27c = 15621, with 468 - c to get
42(468 - c) + 27c = 15621
19656 - 42c + 27c = 15621

19656 - 15c = 15621

 

Subtract 15621 from both sides to get

-15c = -4035

Divide both sides by -15 to get
c = 269

Thus, 269 child and 199 adult tickets were sold.