algebra

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In our math 116 we have a reading problem , it has several steps to it. I have gotten all the way to the end of the assignment and can't get the last questions. it has to do with Buying a Home, the problem is ( you recently started the paper work 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 research online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates , Heavy lifters 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.

  • algebra -

    The simplest way to do it is by tabulation. Create a table with the following headings:
    1. hour
    2. cost for Heavy-Lifters
    3. cost for Quick-Move
    H H-L Q-M
    0 080 000
    1 115 055
    2 150 110
    3 185 165
    4 220 220
    5 255 275
    6 290 330
    ...

    We can see that the cost of Quick-Move catches up with Heavy-Lifter as of the 4 hour, at which time they are equal.

    Another way is to calculate the fixed charge divided by the different in hourly rate, which turns out to be
    80/(55-35) = 4 hours.

    The mathematical way is to formulate two expressions representing the charges.
    HL(t) = 80 + 35t
    QM(t) = 55t
    Solve for the interval where the inequality HL(t)≤QM(t) holds true.

    Your approach depends on what your teacher expects, and how comfortable you are with each method.

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