Question

Ashlee repairs DVD players. She charges $25 to inspect the problem and $20/h to repair the device. a) Write an equation to model this relation. b) Make a table of values. c) Graph this relation. d) Using your graphed relation, how long did it take Ashlee to repair the DVD player if she charged $55? e) Using your graphed relation, how much should Ashlee charge if it takes her 4.5 hours to repair the DVD player?

Answer 1

Given: Ashlee repairs DVD players. She charges $25 to inspect the problem and $20/h to repair the device.

Required: To write the equation for the given model and graph the relation, how long did it take Ashlee to repair the DVD player if she charged $55, and how much should Ashlee charge if it took her 4.5 hours to repair the DVD player.

Explanation: Suppose the total amount charged by Ashlee for a repair is y dollars, and the time taken for repair is denoted by x hours.

Then, inspection charges will be fixed and implied on every repair. For x hours, Ashlee will charge 20x dollars as hourly fees on top of the fixed price.

The total cost of repair can be represented by the equation-

`y=25+20x`

Now we draw a table using the equation and draw the graph as follows-

The graph is

Using the graph, we see that at y=55, x=1.5. Hence it took 1.5 hours to repair if Ashlee charged $55.

Similarly, for x=4.5, the value of y=115. Hence for a repair that takes 4.5 hours, Ashlee should charge $115.

Final Answer: a) The equation is

`y=25+20x`

b)&c) Table and graph are drawn.

d) 1.5 hours

e) $115