Question

Help would be appreciated :)

Mrs. Solar is remodeling a house and is looking for a contractor to do the work. She is getting quotes from three different contractors and will hire one of them based on the total cost. Each company uses a formula to calculate its fees based on the number of hours the work will take.

1. Mrs. Solar modeled Contractor 1's fee formula with the equation y = 50x + 200.
(a) Graph equation y = 50x + 200. Give each axis a label and give the graph a title.
(b) Describe what equation y = 50x + 200 means in the real-world context.
(c) Give three ordered pairs that make the equation true and explain what each ordered pair means in the real-world context.

2. Mrs. Solar modeled Contractor 2's fees with the formula y = 150 + 55x . Mrs. Solar compared Contractor 2's fee to Contractor 1's fee.
(a) What does the difference between 50 and 55 mean in the real-world context?
(b) What does the difference between 200 and 150 mean in the real-world context?
Answer:
 

3. Contractor 3 gives Mrs. Solar the following fee table showing her charges for the contract work.
Number of hours Total cost
2 $120
3 $180
4 $240
5 $300
(a) What is the rate of change? What does this mean in a real-world context?
(b) Write an equation in point-slope form to represent the total cost, y, given x hours.
(c) Graph the equation written in Part (b).
(d) What is the y-intercept? What does this mean in a real-world context?

4. Finally, Mrs. Solar receives the time estimates from each contractor. She wants to have the work done within 5 wk (200 work-hours) of when the work is started, and the sooner the better. She also wants to get a good deal.
(a) Contractor 1's time estimate: 210 h
What is Contractor 1's total cost?
(b) Contractor 2's time estimate: 195 h
What is Contractor 2's total cost?
(c) Contractor 3's time estimate: 185 h
What is Contractor 3's total cost?
(d) Which contractor should Mrs. Solar choose?
Explain your reasoning.
Answer:

Answer 1

1. Graph is attached.

Title: Contractor 1's fee

In the real world it would mean that the total cost (y) is starting at 200 and then 50 per hour.

(1,250) means that she paid 250 for 1 hour

(2,300) means that she paid 300 for 2 hours

(3,350) means that she paid 350 for 3 hours

2. It means that contractor 2 charges 5 more per hour

it means that contractor 1 charges 50 more as a starting fee.

3. rate of change 60, this means that it changes by 60 every time.

y-2=60(x-0)

y intercept is 0

4.

a. x=210, y=10700,y=210(50)+200

b.x=195, y=195(55)+150, y=10875

c.x=185,y=185(60),y=11100

d. She should choose contractor 2 because it's the second cheapest and contractor 1 is over 200 hours.