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 Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.

Question

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 Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.

a) Which mover provides a better deal for 2 hours? How did you arrive at your answer?
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
c) For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.
PLEASE HELP

Answer 1

a) To determine which mover provides a better deal for 2 hours, we can calculate the total cost for both companies.

For Heavy Lifters:
$80 fee + ($35 per hour * 2 hours) = $80 + $70 = $150

For Quick Move:
$55 per hour * 2 hours = $110

Comparing the total costs, we can see that Quick Move charges $110 for 2 hours, while Heavy Lifters charges $150. Therefore, Quick Move provides a better deal for 2 hours.

b) To determine which mover provides a better deal for 15 hours of work, we can calculate the total cost for both companies.

For Heavy Lifters:
$80 fee + ($35 per hour * 15 hours) = $80 + $525 = $605

For Quick Move:
$55 per hour * 15 hours = $825

Comparing the total costs, we can see that Quick Move charges $825 for 15 hours, while Heavy Lifters charges $605. Therefore, Heavy Lifters provides a better deal for 15 hours.

c) To find the values of h (hours) for which Quick Move offers the better deal, we can compare the total costs for both companies.

Let's set up the equation:

$55 per hour * h hours ≤ $80 fee + ($35 per hour * h hours)

Simplifying:

55h ≤ 80 + 35h

20h ≤ 80

h ≤ 4

From the equation, we find that for any value of h (hours) up to and including 4 hours, Quick Move offers a better deal. Beyond 4 hours, Heavy Lifters may provide a better deal.