Question

A furnace repair person charges an initial fee of $80 plus $30 per hour to do repairs.

a. After how many hours would the cost of the repair be at least $320?
b. How many hours did the repair person work if the total bill was $230?

Answer 1

After setting up inequalities for each scenario, we find that for the cost of the repair to be at least $320, at least 8 hours of work are required. When the total bill is $230, the repair person worked for 5 hours.

Step-by-step explanation:

To answer question (a) on how many hours the repair would need to be at least $320 given an initial fee of $80 and an hourly rate of $30, we set up the inequality:

80 + 30h ≥ 320

Subtract 80 from both sides to isolate the hourly term:

30h ≥ 240

Divide both sides by 30 to solve for h:

h ≥ 8

So, the repair would need to be at least 8 hours to cost $320.

To answer question (b) on how many hours the repair person worked for a total bill of $230, we use the equation:

80 + 30h = 230

Subtract 80 from both sides:

30h = 150

Divide both sides by 30:

h = 5

The repair person worked for 5 hours.

Answer 2

A) The repair bill would be at least $320 after 8 hours

B) The repairman would have worked for 5 hours

Step-by-step explanation:

A) Set up your equation with x equaling hours

30x + 80 = 320

subtract 80 to the opposite side of the equation

30x = 240

divide by 30

30x/30 = 240/30

x = 8

B) Set up your equation with x equaling hours

30x + 80 = 230

subtract 80 to the opposite side of the equation

30x = 150

divide by 30

30x/30 = 150/30

x = 5