Advance tickets for a school play went on sale. the price of each student ticket was $4 and everyone else paid $5. on the first day, no more than $80 in tickets were sold. describe and explain the possible values of s, the number of student tickets sold, and e, the number of tickets sold to nonstudents.

1) Step 1

Esblish the equation and restrictions

4s + 5e ≤ 80

s ≥ 0

e ≥ 0

2) Stept 2

Establish the limits for the values os s and e.

If you draw the line 4s + 5e ≤ 80. it will be easier to visualize the following explanation.

The line 4s + 5e = 80 and the two axis bound the values of s and e.

Find the vertices

-  minimum s = 0, => maximum e = [80 - 4s] / 5 = [80 - 0] / 5 = 16

- minimum e = 0 => maximum s = [80 - 5e] / 4 = 80 / 4 = 20 

Solution:

- s, the number of student tickets sold, may be any integer value between 0 and 16, including the limits
- e, the number of tickets sold to nonstudents, may be any integer value between 0 and 20, including the limits