A 5000 seat theater has tickets for sale at 28 and S40 How

A 5000 - seat theater has tickets for sale at $28 and S40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $161, 600? The number of tickets for sale at $28 should be .The number of tickets for sale at $40 should be .

Solution

Let number of tickets for sale at $28 = x and

number of tickets at sale at $40 = y

Then x + y = 5000 .... (1) and

28x+40y = 161600 ... (2)

From (1), y = 5000-x ... (3)

Substitute this in (2),

28x + 40 (5000-x) = 161600

28x + 200000 - 40x = 161600

-12x + 200000 = 161600

-12x = -38400

x = -38400/-12= 3200

Substitute this in (3),

y = 5000 - 3200 = 1800

So x=3200 and y =1800