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
a) To determine which mover provides a better deal for 2 hours, we need to calculate the total cost for each mover.
For Heavy Lifters, the total cost is the base fee plus the hourly rate multiplied by the number of hours:
Total cost = $80 + (2 hours * $35 per hour)
Total cost = $80 + $70
Total cost = $150
For Quick Move, the total cost is simply the hourly rate multiplied by the number of hours:
Total cost = 2 hours * $55 per hour
Total cost = $110
Therefore, for 2 hours of work, Quick Move is the better deal as it offers a lower total cost of $110 compared to Heavy Lifters' total cost of $150.
b) To determine which mover provides a better deal for 15 hours of work, we once again need to calculate the total cost for each mover.
For Heavy Lifters:
Total cost = $80 + (15 hours * $35 per hour)
Total cost = $80 + $525
Total cost = $605
For Quick Move:
Total cost = 15 hours * $55 per hour
Total cost = $825
Therefore, for 15 hours of work, Heavy Lifters is the better deal as it offers a lower total cost of $605 compared to Quick Move's total cost of $825.
c) To find the values of h (hours) for which Quick Move provides the better deal, we can set up an inequality.
Let h be the number of hours worked. The total cost for Quick Move is given by:
Total cost = h hours * $55 per hour
Total cost = $55h
We want the total cost for Quick Move to be less than the total cost for Heavy Lifters, which is $80 + ($35 * h) for any number of hours.
Therefore, we set up the inequality:
$55h < $80 + ($35 * h)
To solve for h, we simplify the equation:
$55h < $80 + $35h
$55h - $35h < $80
$20h < $80
h < $80 / $20
h < 4
Therefore, Quick Move offers the better deal for any number of hours less than 4. In other words, the inequality is h < 4.