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Answer:
- A: j = 25 +55h
- B: m = 50 +30h
- 1 hour
Step-by-step explanation:
We're going to say Job A is the charge at Jim's shop. For h hours, that charge will be the sum of the parts cost and the hourly charge:
j = 25 +55h
Job B is the charge at Myron's shop. Similarly, that charge is ...
m = 50 +30h
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The two charges are equal when ...
j = m
25 +55h = 50 +30h
25h = 25 . . . . . . . . . . . subtract 25+30h from both sides of the equation
h = 1 . . . . . . . . . . divide by 25
The charges are the same at the two shops for 1 hour worked.
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Additional comment
You may be expected to write your equations using y for the charge and x for the hours. I like to use variable names that remind me what they stand for.
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In general, when you have rates that have different fixed fees and different per-quantity costs, the "break even" quantity is the ratio of the difference in fees to the difference in per-quantity costs. Here the parts (fees) differ by $25, and the per-hour cost differs by $25, so the number of hours is 25/25 = 1 to make the charges equal.
