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 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 of work? 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.

Hard to say.

I would say more like 3.24

a) To determine which mover provides a better deal for 2 hours of work, we need to compare the total cost for each company.

For Heavy Lifters:
Total cost = $80 (fee) + $35/hour × 2 hours = $80 + $70 = $150

For Quick Move:
Total cost = $55/hour × 2 hours = $110

Comparing the total costs, we can see that Quick Move provides a better deal for 2 hours of work with a total cost of $110.

b) To determine which mover provides a better deal for 15 hours of work, we need to compare the total cost for each company.

For Heavy Lifters:
Total cost = $80 (fee) + $35/hour × 15 hours = $80 + $525 = $605

For Quick Move:
Total cost = $55/hour × 15 hours = $825

Comparing the total costs, we can see that Heavy Lifters provides a better deal for 15 hours of work with a total cost of $605.

c) To find the values of hours for which Quick Move offers the better deal, we need to find when the total cost for Quick Move is less than the total cost for Heavy Lifters. Let's denote h as the number of hours.

For Quick Move:
Total cost = $55/hour × h hours = $55h

For Heavy Lifters:
Total cost = $80 (fee) + $35/hour × h hours = $80 + $35h

To find when Quick Move offers the better deal, we set up the inequality:

$55h < $80 + $35h

Simplifying the inequality:

$20h < $80

Dividing both sides by $20:

h < 4

Therefore, Quick Move offers a better deal for values of h (hours) less than 4, expressed as the inequality h < 4.