Slide 1.
Part A.
1. Band A: y = 600
2. Band B: y = 1.25x + 350
Part B.
200 students.
Slide 2.
Part A.
Fixed cost = $150
Rate per student served = $6
Part B.
To figure the cost/person, look at the change in cost divided by the change in attendance.
For 100 students, cost = $750.
For 150 students, cost = $1050.
Change in cost = $300
Change in students = 50
Cost per additional student = 300/50 = $6
Assuming the costs are linear, then the price charged for 100 students reflects the cost per student + a 'fixed cost' that applies to the order as a whole.
100 * 6 = $600, so the fixed cost is 750-600 = 150.
We can check this notion by substituting in the other equation.
Does 150*6 + 150 = 1050? Yes.
150*6=900
900+150 = 1050.
Slide 3.
Part A.
She can choose either band, with $9.75 per ticket, if 200 students attend
Part B.
Check the cost using band A and 200 people, including food
600 + 150 + (6*200) =
600 + 150 + 1200 = $1950
Cost per ticket: = 1950/200 = $9.75
Cost using band B, 200 people, including food:
350 + 1.25(200) + 150 + (6*200) =
350 + 250 + 150 + 1200 = $1950
Cost per ticket: 1950/200 = $9.75
This means that Paula can choose either band, and the ticket cost will be the same.
Slide 4.
Part A.
Cost per ticket: $8.50 (of Band A, since it is the cheaper one)
Part B.
Check the cost using band A and 300 people, including food
600 + 150 + (6*300) =
600 + 150 + 1800 = $2250
Cost per ticket: = 2250/300 = $8.50
Cost using band B, 200 people, including food:
350 + 1.25(300) + 150 + (6*300) =
350 + 375 + 150 + 1800 = $2675
Cost per ticket: 2675/300 ≈$8.92
Which means that in this scenario is Band A is less expensive.
