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Math Help - Brain ache

  1. #1
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    Brain ache

    Hi, my brain is aching somewhat over what I am sure is straight forward but I can't see the wood for the trees...help would be appreciated!

    A simple little question really; I am going on holiday with friends (there are 4 couples), and the total for 7 nights is 725. 2 couples are staying 3 nights, one couple 6 nights, and the other couple all 7 nights.

    If you look at a nightly cost (ie 725/7) it is 103.57 per night. Clearly by just splitting this up on a nightly basis (ie 4 ways for 3 nights, 2 ways for the next 3 nights, then one way for the last night) will result in the couple staying for 7 nights paying disproportionately more (in fact the 2 couples staying for 3 nights only pay 77.68!)
    How can we weight it so that the amounts paid are fairer?

    (OK, not strictly homework, but maths nontheless!)
    Last edited by vanishing_point; September 6th 2008 at 07:25 PM. Reason: completion
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  2. #2
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    Quote Originally Posted by vanishing_point View Post
    Hi, my brain is aching somewhat over what I am sure is straight forward but I can't see the wood for the trees...help would be appreciated!

    A simple little question really; I am going on holiday with friends (there are 4 couples), and the total for 7 nights is 725. 2 couples are staying 3 nights, one couple 6 nights, and the other couple all 7 nights.

    If you look at a nightly cost (ie 725/7) it is 103.57 per night. Clearly by just splitting this up on a nightly basis (ie 4 ways for 3 nights, 2 ways for the next 3 nights, then one way for the last night) will result in the couple staying for 7 nights paying disproportionately more (in fact the 2 couples staying for 3 nights only pay 77.68!)
    How can we weight it so that the amounts paid are fairer?

    (OK, not strictly homework, but maths nontheless!)
    How much do you figure the couple staying 7 nights pays? I get \frac{103.57}{4} \times 3 + \frac{103.57}{2} \times 3 + 103.57 = 336.60.

    The 6 nights couple pays \frac{103.57}{4} \times 3 + \frac{103.57}{2} \times 3 = 233.03.

    The 3 nights couples pay 77.68.

    It all seems fair to me. Less couples remaining on a given night means more cost per couple who remain for that night ......

    Now all you have to do is work out who's gonna pay the extra penny to balance the final amount to 725 .....
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  3. #3
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    How about like this.

    Divide the 725 by the number of couplr-nights.
    2 couples for 3 nights = 2*3 = 6 couple-nights
    1 couple for 6 nights = 1*6 = 6 couple-nights
    1 couple for 7 nights = 1*7 = 7 couple-nights
    ---------------------------------------------
    Total = 19 couple-nights.

    725/19 = 38.15789 pounds per couple-night.

    So, for the
    1st night, (2 +1 +1) *(38.15789) = 152.63
    2nd night, (2 +1 +1) *(38.15789) = 152.63
    3rd night, (2 +1 +1) *(38.15789) = 152.63
    4th night, (1 +1) *(38.15789) = ....76.32
    5th night, (1 +1) *(38.15789) = ....76.32
    6th night, (1 +1) *(38.15789) = ....76.32
    7th night, (1) *(38.15789) = ........38.15
    -------------------------------------------
    Total = ...................................752.00

    Oh, how much each couple pays?

    The 2 couples for 3 nights,
    3*(38.15789) = 114.47367
    They will pay 114.47 pounds each......2(114.47) = 228.94 pounds.

    For the couple for 6 nights,
    6*(38.15789) = 228.95 pounds, they will pay

    For the couple for 7 nights,
    7*(38.15789) = 267.11 pounds, they will share.
    Last edited by ticbol; September 6th 2008 at 08:57 PM.
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  4. #4
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    Quote Originally Posted by ticbol View Post
    How about like this.

    Divide the 725 by the number of couplr-nights.
    2 couples for 3 nights = 2*3 = 6 couple-nights
    1 couple for 6 nights = 1*6 = 6 couple-nights
    1 couple for 7 nights = 1*7 = 7 couple-nights
    ---------------------------------------------
    Total = 19 couple-nights.

    725/19 = 38.15789 pounds per couple-night.

    So, for the
    1st night, (2 +1 +1) *(38.15789) = 152.63
    2nd night, (2 +1 +1) *(38.15789) = 152.63
    3rd night, (2 +1 +1) *(38.15789) = 152.63
    4th night, (1 +1) *(38.15789) = ....76.32
    5th night, (1 +1) *(38.15789) = ....76.32
    6th night, (1 +1) *(38.15789) = ....76.32
    7th night, (1) *(38.15789) = ........38.15
    -------------------------------------------
    Total = ...................................752.00

    Oh, how much each couple pays?

    The 2 couples for 3 nights,
    3*(38.15789) = 114.47367
    They will pay 114.47 pounds each......2(114.47) = 228.94 pounds.

    For the couple for 6 nights,
    6*(38.15789) = 228.95 pounds, they will pay

    For the couple for 7 nights,
    7*(38.15789) = 267.11 pounds, they will share.
    If I was in a couple only staying three nights I'd strongly disagree with this calculation. It is based on me subsidising the 6-nights and 7-nights couples .....
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