WORD problems

Question

Both of the following HVAC companies charge a service call fee and an hourly rate, for residential service.

For Richard's HVAC Service, a 6 hour service costs $195 and a 5 hour service costs $170

For Smith's HVAC Service, a 6 hour service costs $170 and a 5 hour service costs $152

For each company, find a linear model for the relationship between the hours spent on a repair and the total charges of a repair. Let,
x  represent the number of hours of service and C represent the cost of the service

The linear model for Richard's HVAC Service:

C=

 

The linear model for Smith's HVAC Service:

C=

The services of these companies would cost the same for____ a hour service. (round to the nearest tenth of an hour)

 

Answer 1

Richard:

  the service call fee is $45.

 

  6 hours service call costs $150 and 5 hour service call costs $125.

  That's $25 per hour.

 

  The linear model is C = $25h + 45

 

 

  Smith's HVAC Service:

   The sevice call is  $62

 

   6 hour service call is  $108 and a 5 hour service call is $90  

  That's $18 per hour.

 

  The linear model is C = 62 + 18h.

 

 They will be equal when: 62 + 18h = 25h + 45

                                

                                    17 = 7h

                                      h = 17/7 = 2 and 3/7 hours = 2.4 hours rounded to the nearest tenth.

 

  Richard:  45 + (17/7)*25 = $105.71

 Smith:  62 + (17/7)*18 = 105.71