Question

A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $155,600?CARDThe number of tickets for sale at $28 should be

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

total seats = 5000

total revenue = $155600

Step 02:

system of equations:

x = # of $28 tickets

y = # of $40 tickets

equation 1:

x + y = 5000

equation 2:

28x + 40y = 155600

x + y = 5000 * (-28)

28x + 40y = 155600

-28x - 28y = - 140000

28x + 40y = 155600

-----------------------------------

12y = 15600

y = 15600 / 12

y = 1300

y in eq. 1:

x + y = 5000

x + 1300 = 5000

x = 5000 - 13000

x = 3700

The answer is:

x = 3700 of $28 tickets

y = 1300 of $40 tickets