Question 9 • FL-1200700-Mathematics for College Algebra MIS
Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5 = 20. What can Casey conclude?
Answer
A
One landscaper charges $20 for 5 hours of work.
B
One landscaper’s hourly rate is $15 lower than the other landscaper’s.
C
Both landscapers charge the same hourly rate and the same fee per job.
D
Both landscapers charge the same hourly rate, but not the same fee per job.
Explanation
The equation 5 = 20 is a contradiction, so the system has no solution: there is no number of hours at which the two cost equations give the same total. For linear cost equations, this occurs when the landscapers have the same hourly rate but different job fees; their cost lines are parallel and never meet. Thus, Casey can conclude that both charge the same hourly rate, but not the same fee per job.
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