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Joe’s Body Shop charges $25 for parts and $50 per hour to fix the brakes on a car. Kathy’s Body Shop charges $70 for parts and $40 per hour for the same type of work.

Let x represent the length of time to fix the brakes on a car.

c. When will the amount charged by Joe and Kathy be the same? Show how you determine your answer.

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Let me just write this simply.
Joe's parts: $25             Joe's hourly rate for brakes: $50/hr
Kathy's parts:$70          Kathy's hourly rate: $40/hr
x = time (to fix the brakes)
So both will start with an initial charge for parts. Joe: $25, and Kathy: $70
Then for each hour, your price goes up...
Here is a table.
               0 hrs      1 hr      2 hrs      3 hrs      4 hrs      5hrs      6 hrs
Joe          25         75         125         175        225       275        325
Kathy       70         110        150        190        230       270        310

So look at the table, notice how joe's prices always end in 5, and Kathy's always end in 0. Because neither Joe's or Kathy's rates go up by a number that ends in 5, they will never be the same.

Answer: never

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