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Math Help - in a hurry...thanks

  1. #1
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    in a hurry...thanks

    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 $72, while one using 1600 cubic feet was billed $108.

    (a) What is the exact charge per cubic foot?


    (b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used.

    (c) How many cubic feet of water used would lead to a bill of $135? Give your answer to the nearest cubic foot.


    ok, i just need some help with this problem....last time i did it, it didn't seem to work right...any help is greatly appreciated...thanks


    mathlete
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathlete View Post
    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 $72, while one using 1600 cubic feet was billed $108.

    (a) What is the exact charge per cubic foot?


    (b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used.

    (c) How many cubic feet of water used would lead to a bill of $135? Give your answer to the nearest cubic foot.


    ok, i just need some help with this problem....last time i did it, it didn't seem to work right...any help is greatly appreciated...thanks


    mathlete
    it seems obvious that there is a linear relationship here between the charge and the amount of water used.

    so start with C = mw + b

    where C is the charge, m is the slope (the charge per cubic foot of water used), and b is the y-intercept (the fixed charge), and w is the amount of water used in cubic feet

    now we need to find m and b. once we have those, we can answer the questions.

    we are given two points on this line: (w_1,C_1) = (1000, 72) and (w_2,C_2) = (1600, 108)

    we can use these two points to find the slope, and then use that to find the y-intercept
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    it seems obvious that there is a linear relationship here between the charge and the amount of water used.

    so start with C = mw + b

    where C is the charge, m is the slope (the charge per cubic foot of water used), and b is the y-intercept (the fixed charge), and w is the amount of water used in cubic feet

    now we need to find m and b. once we have those, we can answer the questions.

    we are given two points on this line: (w_1,C_1) = (1000, 72) and (w_2,C_2) = (1600, 108)

    we can use these two points to find the slope, and then use that to find the y-intercept

    ok i got b and c, can you give me more on how to find the exact charge per cubic feet
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathlete View Post
    ok i got b and c, can you give me more on how to find the exact charge per cubic feet
    the exact charge per cubic foot is m

    (you're not supposed to be finding C, C i sthe output. we leave it as a variable
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