(Step-by-Step) Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required


Question: Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job and let y denote the total cost to the customer.

  1. Find the equation that expresses y in terms of x.
  2. Determine and .
  3. Construct a table similar to Table 14.1 for the x-value 0.5, 1, and 2.25 hours.
    Table 14.1
    Time (hr)
    x
    Cost ($)
    y
    5.0
    7.5
    15.0
    20.0
    22.5
    125
    175
    325
    425
    475
  4. Draw a graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line.
  5. Apply the graph from part (d) to estimate visually the cost of a job that takes 1.75 hours. Then calculate that cost exactly by using the equation from part (a).

Solution:

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