a) Four inequalities
- Variables:
number of adult tickets = a
number of student tickets = s
- An adult ticket costs $15 and a student ticket costs $11
=> sale = 15a + 11s
- The auditorium will seat 300 ticket-holders =>
(1) a + s ≤ 300
- The drama club wants to collect at least $3630 from ticket sale =>
(2) 15a + 11 s ≥ 3630
(3) a ≥ 0
(4) s ≥ 0
Graph
- Draw the s-axis, and highlight the positive part (s ≥ 0)
- Draw the a- axis, and highlight the positive part (a ≥ 0)
- Draw the line a + s = 300 ; use the points (0,300) and (300, 0) which are the extremes of the line
- Shadow the region below the line (a + s ≤ 300)
- Draw the line 15 a + 11 s = 3630; use the points (0, 242) and (330,0) which are the extrems of the line
- Shadow the region above the line (15a + 11s ≥ 3630)
The solution is the region that you shadowed twice: a triangle, located between the two inclined lines, at the left of the shadowed region.
b) List three combination of tickets that satisfy the inequalities
Choose some points that are in the solution region. For example:
1) s = 10, a = 250
2) s = 40, a = 240
3) s = 0, a = 300
