Mary’s yard is a mess. She needs to hire someone to prune her trees and shrubs. A landscaping service she calls quotes her a price of $15 consultation fee plus $8 an hour for the actual work. Mary’s neighbor has offered to help her out. She doesn’t charge a consultation fee, but does charge $10 an hour for her work.
Who do you think Mary should hire for a 3-hour job? When, if at all, would it be more economical to hire the other service.
Service:
15 + (3 * 8) = ?
Neighbor:
10 * 3 = ?
service = 29
neighbor = 30
To determine who Mary should hire for a 3-hour job, let's calculate the total cost for each option:
1. Landscaping Service:
- Consultation fee: $15
- Hourly rate: $8
- Total cost for 3 hours: 3 hours * $8/hour = $24
- Total cost: $15 + $24 = $39
2. Neighbor:
- Consultation fee: $0
- Hourly rate: $10
- Total cost for 3 hours: 3 hours * $10/hour = $30
Based on the calculations, hiring the neighbor for a 3-hour job would cost Mary $30, while hiring the landscaping service would cost her $39.
Therefore, Mary should hire her neighbor since it would be more economical for a 3-hour job.
However, if the job were to take longer than 3 hours, it is possible that hiring the landscaping service would become more economical.
To determine who Mary should hire for a 3-hour job, we need to compare the total cost of hiring the landscaping service and the cost of hiring her neighbor.
For the landscaping service:
- Consultation fee: $15
- Hourly rate: $8
Total cost for 3 hours of work: $15 + ($8 * 3) = $15 + $24 = $39
For Mary's neighbor:
- No consultation fee
- Hourly rate: $10
Total cost for 3 hours of work: ($10 * 3) = $30
Therefore, Mary should hire her neighbor for a 3-hour job as it would cost her $30, which is cheaper than the $39 cost of hiring the landscaping service.
To determine when it would be more economical to hire the other service, we need to compare the pricing of the landscaping service and Mary's neighbor based on the number of hours needed for the job. Let's assume the number of hours is "x".
For the landscaping service:
Total cost = $15 + ($8 * x) = $15 + $8x
For Mary's neighbor:
Total cost = $10 * x = $10x
To find the point at which the costs are equal, we can equate the two equations and solve for "x":
$15 + $8x = $10x
Subtract $8x from both sides:
$15 = $2x
Divide both sides by $2:
x = $15 / $2 = 7.5
Therefore, it would be more economical to hire the landscaping service if Mary needs the job to be done in more than 7.5 hours.