Question

A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of 153800.

Answer 1

The number of tickets for sale at $26 should be 3300

The number of tickets for sale at $40 should be 1700

Explanation:

Use 2 equations to represent the modifiers within the problem:

`5000 = a + b \\ 153800 = 26a + 40b`

Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.

`5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)`