A computer repair shop charges a flate rate of 50$ plus $35 per hour spent repairing each computer. LEt h be the number of hours spent repairing a computer. Use function notation to write an equation that gives the total charges for repairing a compujter as a function of h. Graph the function.
b) How much will the repair shop charge if the shop does 2.5 hours of work?
c) The repair shop charges 172.50 to repair a computer. How many hours did the shop work on the computer?
50 + 35h = cost
Cannot graph here.
b. Insert hours and solve.
c. Insert cost and solve.
To write the equation that gives the total charges for repairing a computer as a function of h (the number of hours spent repairing), we can start with the flat rate of $50 and add $35 per hour spent.
Let's use C(h) to represent the total charges as a function of h. The equation for C(h) will be:
C(h) = 50 + 35h
To graph the function, we can plot points on a coordinate plane. The x-axis will represent the number of hours (h), and the y-axis will represent the total charges (C).
Here are a few points we can plot to draw the graph:
- (0, 50): When no hours are spent repairing (h = 0), the total charges are $50.
- (1, 85): If 1 hour is spent repairing (h = 1), the total charges will be $50 + $35 = $85.
- (2, 120): If 2 hours are spent repairing (h = 2), the total charges will be $50 + 2($35) = $120.
By plotting these points and connecting them with a straight line, we can obtain the graph of the function C(h).
b) To calculate how much the repair shop will charge for 2.5 hours of work, we substitute h = 2.5 into the equation:
C(2.5) = 50 + 35(2.5)
C(2.5) = 50 + 87.5
C(2.5) = 137.5
Therefore, the repair shop will charge $137.50 for 2.5 hours of work.
c) To find the number of hours the shop worked on the computer if they charged $172.50, we need to solve the equation C(h) = 172.50 for h:
172.50 = 50 + 35h
122.50 = 35h
h = 122.50 / 35
h ≈ 3.50
Therefore, the shop spent approximately 3.50 hours working on the computer.