Cheap Car Shop charges $77 for parts and $31 per hour of labor for a repair job. Best Repair in Town charges a flat fee of $150 for the same job. Write a system of equations to represent the situation.

Let's call x the number of hours spent on the job.

Cheap car shop charges a total (we'll call it T) equal to 77+31x.

Best Repair in Town charges 150.

The sistem is:

T=77+31x

T=150

Solving it you can find the number of hours x that would take Cheap Car Shop to do the job and have a pay equal to the one of Best Repair in town. Under x, Cheap car shop is more convenient, over x, Best Repair in town is more convenient.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is