Question

The Social Justice Club is going to rent a mammoth barbeque to cook the hot dogs for the hot dog sale. After contacting three rental companies in town, you have found out that each one will deliver and pick up their barbeque. The cost of propane is included in the rental. The rental costs are indicated below.

Rental A: $15/h

Rental B: $5/h + 50

Rental C: $9/h + 20

Student selling hot dogs at a table.
Write an equation that models the rental cost, C, for each company.
Graph all three models onto the same set of coordinate axis.
Which rental company should be chosen if you use the barbeque during lunch (11:05 - 12:30) and keep the barbeque to continue sales during the football game that will end about 4:30? Justify your answer.
Which rental company should be chosen if your school lunch hours run from 11:05 - 12:30? Justify your answer.
Which rental company should be chosen if your school returned the barbeque the following day? Justify your answer.

Answer 1

(A)Cost of Rental A, C= 15h

Cost of Rental B, C=5h+50

Cost of Rental C, C=9h+20

(B)

i. Rental C

ii. Rental A

iii. Rental B

Explanation:

Let h be the number of hours for which the barbeque will be rented.

Rental A: $15/h

• Cost of Rental A, C= 15h

Rental B: $5/h + 50

• Cost of Rental B, C=5h+50

Rental C: $9/h + 20

• Cost of Rental C, C=9h+20

The graph of the three models is attached below

(b)11.05-4.30

When you keep the barbecue from 11.05 to 4.30 when the football match ends.

Number of Hours = 4.30 -11.05 =4 hours 25 Minutes = 4.42 Hours

• Cost of Rental A, C= 15h=15(4.42)=$66.30

• Cost of Rental B, C=5h+50 =5(4.42)+50=$72.10

• Cost of Rental C, C=9h+20=9(4.42)+20=$59.78

Rental C should be chosen as it offers the lowest cost.

(c)11.05-12.30

Number of Hours = 12.30 -11.05 =1 hour 25 Minutes = 1.42 Hours

• Cost of Rental A, C= 15h=15(1.42)=$21.30

• Cost of Rental B, C=5h+50 =5(4.42)+50=$57.10

• Cost of Rental C, C=9h+20=9(4.42)+20=$32.78

Rental A should be chosen as it offers the lowest cost.

(d)If the barbecue is returned the next day, say after 24 hours

• Cost of Rental A, C= 15h=15(24)=$360

• Cost of Rental B, C=5h+50 =5(24)+50=$170

• Cost of Rental C, C=9h+20=9(24)+20=$236

Rental B should be chosen as it offers the lowest cost.