An outdoor amphitheatre has 20000 seats Ticket prices are 8

An outdoor amphitheatre has 20,000 seats. Ticket prices are $8, $12 and $20. How many tickets of each price should be sold (assuming all seats can be sold) to bring in a return of $300,000? Make a table to indicate 3 sets of the coordinated values for x_1, x_2, and x_3.

Solution

Let x₁ be the number of tickets with price $8 ,x₂be the number of tickets with price $12 and x₃ be the number of tickets with price $20

Therefore according to question

x₁+x₂+x₃=20000

8x₁+12x₂+20x₃=300000

when x₁=2000

x₂+x₃=18000,12x₂+20x₃=300000-16000=284000

Solving these two equations we get

x₂=9500,x₃=8500

when x₁ =4000

we get x₂+x₃=16000, 12x₂+20x₃=300000-32000=268000

Solving these two equations we get x₂=6500   and x₃=9500

when x₁=8000

x₂+x₃=12000,12x₂+20x₃=300000-64000=236000

Solving these two equations,we get

x₂=500 and x₃= 11500

x1	2000	4000	8000
x2	9500	6500	500
x3	8500	9500	11500