Question

Mrs. Solar is remodeling a house and is looking for a contractor to do the work. She is getting quotes from 3 different contractors, and will hire one of them based on the total cost. Each company uses a formula to calculate its fees based on the number of hours the work will take.

2. Mrs. Solar modeled Contractor 2’s fees with the formula y = 150 + 55x. Mrs. Solar compared Contractor 2’s fee to Contractor 1’s fee.
(a) What does the difference between 50 and 55 mean in the real-world context?
(b) What does the difference between 200 and 150 mean in the real-world context?

Answer 1

Contractor 1: y = 200 + 50x
Contractor 2: y = 150 + 55x

50 and 55 are the variable costs incurred in doing the project. These costs will only be implemented when x changes. X is the variable that may represent the number of hours worked, number of people added to complete the task.

200 and 150 are the fixed cost of the project. Mrs. Solar must pay the cost regardless of the changes happening in x.

For example: Both contractors need to add 15 additional people to complete the task. Then:
Contractor 1 : y = 200 + 50(15) = 200 + 750 = 950
Contractor 2 : y = 150 + 55(15) = 150 + 825 = 975 è Contractor 1 is the best option:
If x = 10 additional people
Contractor 1: y = 200 + 50(10) = 200 + 500 = 700
Contractor 2: y = 150 + 55(10) = 150 + 550 = 700 è Any contractor is the best option
If x = 5 additional people
Contractor 1: y = 200 + 50(5) = 200 + 250 = 450
Contractor 2: y = 150 + 55(5) = 150 + 275 = 425 è Contractor 2 is the best option