Question

A theater sold 900 tickets to a play. Floor seats cost $12 each and balcony seats $10 each. Total receipts were $ 9,780. How many of each type of ticket were sold?

Answer 1

A theater sold 390 floor seats and 510 balcony seats.

Step-by-step explanation:

Let's assume that the number of floor seats sold is x and the number of balcony seats sold is y.

According to the given information, the total number of tickets sold is 900, so we have the equation:

x + y = 900

Next, let's calculate the total revenue from selling tickets:

Revenue from floor seats: 12x

Revenue from balcony seats: 10y

According to the given information, the total receipts were $9,780, so we have the equation:

12x + 10y = 9780

We now have a system of equations:

x + y = 900

12x + 10y = 9780

We can solve this system of equations by substitution, elimination, or graphing.

Using the substitution method, we can solve one equation for x and substitute it into the other equation:

x = 900 - y

Substituting x into the second equation:

12(900 - y) + 10y = 9780

Simplifying:

10800 - 12y + 10y = 9780

-2y = -1020

y = 510

Substituting y = 510 back into x + y = 900:

x + 510 = 900

x = 390

Therefore, 390 floor seats and 510 balcony seats were sold.

Answer 2

Floor tickets: 390 (390x$12=$4680)

Balcony tickets: 510
(510x$10=$5100)

390+510=900
$4680+$5100=$9780