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Math Help - Check please, and take a look at other questions..

  1. #1
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    Check please, and take a look at other questions..

    Monica is planning a party to be held at the local community hall. She is told by the hall manager that the cost, C, varies partially with the number of guests, n, that attend; that is, for each additional guest, the cost increases by the same amount.

    People Cost

    25 $70

    50 $120

    100 $220

    Determine the equation of the variation in the form of C = mn + b. State any restrictions on n.

     C1 = 70 = 25m + b
     C2 = 120 = 50m + b
     25m = 50 => m = 2 => b = 20

    C3 220 = 100m + b
    50m = 100 => m = 2 => b = 20

    Thus, the equation is C = 2n + 20

    Ok, done, simple enough.

    What is the signifigance of b?

    B indicates a fixed cost, not dependent on N, such as a Base rental fee.

    Use the formula to fill in the table.

    People Cost

    1 $22
    2 $24
    3 $26
    4 $28

    What kind of sequence is illustrated in this table?

    an arithmetic sequence, aka a linear sequence

    The manager tells Monica that during the last 40 days, the hall has been rented 40 times. The number of guests for those 40 rentals can be arranged to form the following sequence:

    11,12,13, ..., 49,50

    What is the total amount of money collected by the hall manager for those 40 days?
    Last edited by zoso; July 21st 2006 at 08:21 AM.
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by zoso
    ...The manager tells Monica that during the last 40 days, the hall has been rented 40 times. The number of guests for those 40 rentals can be arranged to form the following sequence:
    11,12,13, ..., 49,50
    What is the total amount of money collected by the hall manager for those 40 days?
    Hello, zoso,

    a) the hall has been rented for 40 days, so you've fixed cost of 40 * 20 = 800 $

    b) There are \sum_{\csub{i=1}}^{40}{(i+10) = 1220\ guests

    For each guest has to be payed 2 $, total amount: 800 $ + 1220 * 2 $ = 3240 $

    Greetings

    EB
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