Last One

kmomma1999

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Joined
Sep 11, 2008
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This is the last one for tonight.

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.

Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?

My answer:
For 2 hours Quick Move is the better deal. I multiplied the hourly rate from each company by two, but for Heavy Lifters I also had to add in the 80 fee. Quick Movers was 110 and Heavy Lifters was 150

Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?

My answer:
For 15 hours Heavy Lifters is the better deal. I multiplied both hourly rates by 15 and for heavy lifters had to add the 80 fee. For Heavy lifters the price would be 605 and for Quick Move the price would be 675

For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer

Now that I have reached the last question, I have realized that while I may have the right answers for the first two parts of this question, there is probably an equation that I should have come up with. I am unsure of how to formulate this equation. Any help would be appreciated. Thanks!
 
You can use an "equation" to determine the "even" point:
80 + 35h = 55h
20h = 80
h = 4

So one is cheaper if hours are lesser than 4, other is cheaper if hours greater than 4; ok mom?
 
Denis explained it pretty well. Just include the < symbol. As an inequality, we want an expression that will show Quick Move is less than the Heavy Lift.

\(\displaystyle 55x<80+35x\)

Solve for x. That will be the values for which Quick Move is cheaper.
 
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