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Homework Help: Situation described by a function.

  1. Aug 23, 2006 #1
    Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $90, while one using 1600 cubic feet was billed $105.

    a) What is the charge per cubic foot?
    b) Write an equation for the total cost of a resident's water as a function of cubic feet of water used.
    c) How many cubic feet of water used would lead to a bill of $130?



    All right, here are my attempts. I first did the whole find the slope thing.
    (1000, 90) , (1600, 105)
    (105 - 90) / (1600 - 1000) = 15/600 = 1/40
    So, this means that for $1, you get 40 cubic feet. (but that isn't the question... the question is how much does 1 cubic foot cost.....)

    that was the first thing that confused me.. but i decided that maybe i was going in the right direction, so I tried to keep working... by trying to write the equation.

    y = mx + b
    90 = (1/40)(1000) + b
    90 = 25 + b
    b = 65
    y = (1/40)x + 65

    now that i had the equation, i plugged in a 1 for x to see what 1 cubic foot would cost.

    y = (1/40) (1) + 65
    y = 1/40 + 65
    y = $65.025

    so, now i subtracted that amount from the fixed amount
    $65.025 - $65 = $.025 or 2.5 cents

    What confuses me is ... .025 = 1/40 (my slope), but i thought the slope meant 1 dollar for 40 cubic feet, now 1 cubic foot for .025 cents. And if it does work out, i just would like to know why you can switch the variables around like that so easily.

    so.. to continue..

    i have the answers for a and b.. time to work out c.
    130 = (1/40)x + 65
    x = 2600

    a) 2.5 cents/cubic ft
    b)y = (1/40)x + 65
    c)2600 cubic feet of water used

    I think it's all correct, but i seriously want to know why the variables can be switched .. because the slope should be $1 for 40 cubic feet, and not 2.5 cents for 1 cubic foot. Yes, it does make sense, i just don't know why.. lol..

    thanks in advance.
     
  2. jcsd
  3. Aug 23, 2006 #2

    0rthodontist

    User Avatar
    Science Advisor

    You just said what it cost: $(1/40). How many cents is that?
    1 dollar for 40 cubic feet is the same as 2 dollars for 80 cubic feet, or 1/10 dollars (10 cents) for 4 cubic feet, or 1/40 of a dollar (2.5 cents) for 1 cubic foot. So long as you keep them in proportion you can scale them.
     
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