a) The sales representative here tells you they also have two floor plans available, but they only have 54 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.
X+Y=54 or Y=(54-x)with the substitution.
b) The representative tells you that floor plan #1 sells for $180,000 and floor plan #2 sells for $250,000. She also mentions that all the available houses combined are worth $11,400,000. Write an equation that illustrates this situation. Use the same variables you used in part A.
180,000x+250,000y=11,400,000
c) Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Substitute (54-x) for y, find x
180,000x + 250,000(54-x)=11,400,000
180,000x + 1,350,0000- 250,000 = 11,400,000
180,000x – 250,000=11,400,000-1,350,000
70,000x= 10,050,000
X=
3. You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifters charges a fixed $100 fee plus $45 per hour. Quick Move charges $85 per hour with no additional fees.
a) Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
b) Which mover provides a better deal for 5 hours of work? How did you arrive at your answer?
a) To determine which mover provides a better deal for 2 hours of work, we need to calculate the total cost for each mover.
For Heavy Lifters:
Fixed fee = $100
Hourly rate = $45
Total cost = Fixed fee + (Hourly rate * Number of hours)
Total cost for 2 hours with Heavy Lifters = $100 + ($45 * 2) = $190
For Quick Move:
Hourly rate = $85
Total cost = Hourly rate * Number of hours
Total cost for 2 hours with Quick Move = $85 * 2 = $170
Therefore, Quick Move provides a better deal for 2 hours of work as their total cost is $170, which is lower than Heavy Lifters' total cost of $190.
b) To determine which mover provides a better deal for 5 hours of work, we follow the same process as in part a.
Total cost for 5 hours with Heavy Lifters = $100 + ($45 * 5) = $325
Total cost for 5 hours with Quick Move = $85 * 5 = $425
Therefore, Heavy Lifters provides a better deal for 5 hours of work as their total cost is $325, which is lower than Quick Move's total cost of $425.