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.
For a or b, calculate the costs for both companies and compare.
The time which they would both be equal is found by
80 + 35x = 55x
Work from there to get your inequality.
I hope this helps. Thanks for asking.
To determine which mover provides a better deal for a given number of hours, we need to calculate the total cost for each company and compare the results.
a) For 2 hours of work:
- Heavy Lifters charges a $80 fee plus $35 per hour. Therefore, the total cost would be $80 + (2 hours * $35/hour) = $80 + $70 = $150.
- Quick Move charges $55 per hour with no additional fees. Thus, the total cost for 2 hours of work would be 2 hours * $55/hour = $110.
Comparing the total costs, Quick Move charges $110 for 2 hours of work, while Heavy Lifters charges $150. Therefore, Quick Move is the better deal for 2 hours of work.
b) For 15 hours of work:
- Heavy Lifters charges a $80 fee plus $35 per hour. Hence, the total cost would be $80 + (15 hours * $35/hour) = $80 + $525 = $605.
- Quick Move charges $55 per hour with no additional fees. Therefore, the total cost for 15 hours of work would be 15 hours * $55/hour = $825.
Comparing the total costs, Heavy Lifters charges $605 for 15 hours of work, while Quick Move charges $825. Therefore, Heavy Lifters is the better deal for 15 hours of work.
c) To determine for what values of h (hours) Quick Move offers the better deal, we need to find the tipping point where the total cost of both movers becomes equal. Let's set up an equation:
$80 + (h hours * $35/hour) = h hours * $55/hour
Simplifying the equation:
$80 + 35h = 55h
Subtracting 35h from both sides:
$80 = 20h
Dividing both sides by 20:
4 = h
Therefore, Quick Move offers the better deal for values of h (hours) less than 4. As soon as the number of hours exceeds 4, Heavy Lifters becomes the better deal. Hence, the inequality expressing this relationship is h < 4, meaning the number of hours should be less than 4 for Quick Move to offer the better deal.