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? One landscaper charges $20 for 5 hours of work. One landscaper’s hourly rate is $15 lower than the other landscaper’s. Both landscapers charge the same hourly rate and the same fee per job. Both landscapers charge the same hourly rate, but not the same fee per job.
Answers
Both landscapers charge the same hourly rate, but not the same fee per job
"To determine: The conclusion that Casey arrives about hiring the landscaper
Given Data:
Each landscaper quotes an hourly wage along with a fee for each job.
Resulting equation after solving a "system of linear equations" is 5=20
Formulas to be used:
Solving a "system of Linear equations" by substitution
If x and y are two variables used in the equations, then
1) In at least one of the two equations, we need to get one variable solved, let say y is solved.
2) Substitute the resulting expression in terms of x for y in the second equation
3) Solve the two equations to get the value of x
4) Substitute this value of x in the y that we got in Step 1, so that we get the value of y
Calculation:
On graphing the values after Casey solves the two equations, Casey can conclude that both the lines would be parallel. This implies that they would have the "same slope" or "hourly rate". However, the y-intercepts or fee per job, would be different
Hence, Answer is 'Both landscapers charge the same hourly rate, but not the same fee per job."