Question

Your total cost C to have a TV repairperson from "Mr. Fixit TV" come to your house to fix your TV is a $175 plus an additional $60.00 for each hour h that they are at your house. Your total cost C to have a TV repairperson from "I KNOW VS" come to your house to fix your TV is a $100 plus an additional $75.00 for each hour h that they are at your house.

a) Write an equation that represents the cost after t hours for each company.
b) How long does it take to the costs to be equal for each company?
c) Which company would you use? Explain.
d) Is this discrete or continuous? Explain your reasoning.
e) Compare the costs for each hour.

Answer 1

a) The equations representing the cost after t hours for each company are C = 175 + 60t and C = 100 + 75t. b) It takes 5 hours for the costs to be equal for each company. c) Which company to use depends on personal preference and budget, with Mr. Fixit TV charging less per hour and I KNOW VS having a lower initial cost. d) This is a continuous situation because the cost can vary continuously. e) The cost per hour is higher for I KNOW VS than Mr. Fixit TV.

Step-by-step explanation:

a) To write an equation that represents the cost after t hours for each company, we can use the given formulas: Mr. Fixit TV: C = 175 + 60t and I KNOW VS: C = 100 + 75t.

b) To find the time it takes for the costs to be equal for each company, we set the two equations equal to each other and solve for t: 175 + 60t = 100 + 75t. 15t = 75, t = 5. So it takes 5 hours for the costs to be equal for each company.

c) Which company to use depends on personal preference and budget. If time is the main concern, Mr. Fixit TV may be preferred as they charge less per hour. If cost is the main concern, I KNOW VS may be preferred as they have a lower initial cost.

d) This situation is continuous because the cost can vary continuously depending on the number of hours.

e) Comparing the costs, Mr. Fixit TV charges $60 per hour while I KNOW VS charges $75 per hour. So the cost per hour is higher for I KNOW VS.