1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.

a. What equation relates the number of students x to the theater's income I?

b. What equation relates the theater's operating expenses E to the number of students x?

c. Copy and complete the table below.

Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.

e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.

f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”

g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.

h. Find the number of students that make each of the following inequality statements true.

i. E < 255

ii. I > 675