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Math Help - Word Problem

  1. #1
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    Word Problem

    Not sure what I am doing wrong..

    Question:

    Terry makes and sells necklaces. He has observed over time that when the price is $ 9 each, he sells an average of 30 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost $8. Express his profit P as a function of x, the number of necklaces sold.
    Answer: P(x)=

    What I have:

    Profit function is revenue minus cost. Thus:

    P(x)=R(x)-C(x)

    And R(x)= P*Q Where P is Price and Q is quantity.

    My Formula:


    Simplify:


    What am I missing?
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  2. #2
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    mvho!

    Terry makes and sells necklaces.
    He has observed over time that when the price is $9 each, he sells an average of 30 per day.
    If he increases the price, then his average sales fall by 3 per day for each dollar increase.
    The materials for each necklace cost $8.
    Express his profit P as a function of x, the number of necklaces sold.

    What I have:

    Profit function is Revenue minus Cost: . P(x)\:=\:R(x)-C(x)

    And R(x)\:=\:P\cdot Q where P is Price and Q is Quantity.

    My formula: . P(x) \:=\:(9+x)(30-3x) - 8(30-3x) . . . . Correct!

    Simplify: . P(x) \:=\:-3x^2 + 27x + 30 .??

    What am I missing? . . . . some arithmetic?

    You had: . P(x) \:=\:(9+x)(30-3x) - 8(30-3x)

    . . . . . . . . . . . = \;270 \;{\color{red}-\;27x} + 30x - 3x^2 - 240 \;{\color{red}+\;24x}

    . . . . . . . . . . . = \;-3x^2 \;{\color{red}-\;3x} + 30

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  3. #3
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    LOL

    That's actually the answer I had previously also but its not accepting neither. I don't see how you get -3x as opposed to 27x though. Because you have -27x+30x+24x=27x?


    So I am thinking it is my formula. Maybe I should be expressing "X" as something else?

    Did I do this part correctly at least?

    "Express his profit P as a function of x, the number of necklaces sold."
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  4. #4
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    Hello mvho
    Quote Originally Posted by mvho View Post
    Not sure what I am doing wrong..

    Question:

    Terry makes and sells necklaces. He has observed over time that when the price is $ 9 each, he sells an average of 30 per day. If he increases the price, then his average sales fall by 3 per day for each dollar increase. The materials for each necklace cost $8. Express his profit P as a function of x, the number of necklaces sold.
    Answer: P(x)=

    What I have:

    Profit function is revenue minus cost. Thus:

    P(x)=R(x)-C(x)

    And R(x)= P*Q Where P is Price and Q is quantity.

    My Formula:

    No. In this formula, x represents the number of dollars price increase.
    Simplify:


    What am I missing?
    If the price he sells at is $ (9+y), then he can expect to sell (30-3y) necklaces. So if he sells x necklaces

    x = 30 -3y

    \Rightarrow y = 10-\tfrac13x

    \Rightarrow he sells at $ (9+10-\tfrac13x) = $ (19-\tfrac13x)

    So his profit is $ (19-\tfrac13x)x -8x = $ (11x -\tfrac13x^2)

    Grandad
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  5. #5
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    All the previous questions followed the same pattern except this one. I'll remember to be more careful with my variables next time.

    Express, y in terms of x and substitute; I'll remember that!

    Thanks everyone that viewed and replied.
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