Question 9 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY
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 is equal to 20 What can Casey conclude?
Answer
A
Both landscapers charge the same hourly rate and the same fee per job.
B
One landscaper’s hourly rate is 15 dollars lower than the other landscaper’s.
C
Both landscapers charge the same hourly rate, but not the same fee per job.
D
One landscaper charges 20 dollars for 5 hours of work.
Explanation
The equation 5 = 20 is false, so the system has no solution: there is no number of hours for which the two landscapers’ costs are equal. In a system comparing cost equations, substitution leads to a contradiction when the hourly rates are the same but the job fees differ. Casey can conclude that both landscapers charge the same hourly rate, but not the same fee per job.
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