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. (Set up and solve a system of equations to answer this question.)
Answer
A
Mary should hire her neighbor; if there was more than 7.5 hours of work she should hire the landscaping service.
B
Mary should hire her neighbor; if there was more than 4.2 hours of work she should hire the landscaping service.
C
Mary should hire the landscaping service; if there was more than 7.5 hours of work she should hire her neighbor.
D
Mary should hire the landscaping service; if there was more than 4.2 hours of work she should hire her neighbor.
Explanation
Let h be the number of work hours. The landscaping service costs 15 + 8h dollars, while the neighbor costs 10h dollars. For 3 hours, the service costs $39 and the neighbor costs $30, so Mary should hire her neighbor. Set the costs equal: 15 + 8h = 10h, which gives h = 7.5; beyond 7.5 hours, the landscaping service is cheaper because its hourly rate is lower.
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