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.

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.

AWhat does the difference between 50 and 55 mean in the real-world context?
BWhat does the difference between 200 and 150 mean in the real-world context?

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