Gallery Problems Exercise

Carpet Cleaning

Work Time

Carpet Cleaning

Mr. Adams’s brother owns a carpet cleaning business. Problems 1–4 show different jobs his company was hired to do. Answer the questions for each job using the following for each situation.

  • Let a represent the flat fee, in dollars, for coming to the house.
  • Let b represent the number of hours spent at the house.
  • Let c represent the charge, in dollars, for each hour spent at the house.
  • Let d represent the total cost, in dollars, of the job.
  1. Determine the total cost of a job.
    • If a = 60, b = 4, and c = 50, write an equation for calculating the total cost, d, of this job.
    • Solve your equation to find the total cost of this job.
  2. Determine the number of hours spent at the house.
    • If a = 40, c = 30, and d = 220, write an equation for calculating the number of hours, b, the cleaners spent on this job.
    • Solve your equation to find the number of hours the cleaners spent on this job.
  3. Determine the hourly charge for a job.
    • If a = 50, b = 7, and d = 610, write an equation for calculating the charge, c, for each hour this job took.
    • Solve your equation to find the hourly charge for this job.
  4. Determine the flat fee the cleaners charged for coming to a house.
    • If b = 3, c = 35, and d = 150, write an equation for calculating the flat fee, a, the cleaners charged for this job.
    • Solve your equation to find the flat fee the cleaners charged for this job.
  5. Write all the algebraic equations you can to show the relationships between a, b, c, and d for the carpet cleaning business of Mr. Adams’s brother.