Final answer:
To solve Johnny's problem, the system of equations is set up using the service call charges and hourly rates of 'Plug it in' and 'Lights on'. Solving the system, we find that after 2 hours the total charge of both electricians will be the same.
Step-by-step explanation:
To solve Johnny's dilemma, we first need to set up a system of equations based on the information provided for each electrician's pricing structure. Let x represent the number of hours of work required, and y be the total cost for the service. The correct system of equations for the electricians 'Plug it in' and 'Lights on' respectively are:
- Plug it in: 25 + 15x = y
- Lights on: 35 + 10x = y
These two equations represent the total cost of hiring each electrician, where 25 and 35 are the fixed service call charges, and 15 and 10 are the hourly rates charged by 'Plug it in' and 'Lights on' respectively.
To find the number of hours after which both electricians would charge the same amount, we would set the right sides of the two equations equal to each other and solve for x:
25 + 15x = 35 + 10x
If we subtract 10x from both sides, we get 25 + 5x = 35. Subtracting 25 from both sides, we get 5x = 10. Dividing by 5, we obtain x = 2.
This result indicates that after 2 hours of work, both electricians will have the same total charge.