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Math Help - Couple word problems im having trouble setting up

  1. #1
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    Couple word problems im having trouble setting up

    Im having a hard to figuring out how to set these up:


    Regrind, INC, used typewriters platens. The variable cost to regrind each platen is $1.40. The total cost to regrind 70 platens is $400. Find the linear cost function to regrind platens. If regrind platens sell for $9.40 each, how many must be reground and sold to break even?



    ----------------------------------------

    A rug is fit into a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?






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  2. #2
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    Hello, Jerry99!

    Did you make a sketch?


    \text{A rug is fit into a room so that a border of even width is left on all sides.}
    \text{If the room is 12 ft}\tomes\text{ 15 ft and the area of the rug is 108 ft}^2,
    . . \text{how wide will the border be?}
    Code:
    
          : - - -  15 - - - :
        - *-----------------* -
        : |   :         :   | x
        : | - *---------* - | -
        : |   |         |   | :
        12|   |         |   |12-2x
        : |   |         |   | :
        : | - *---------* - | -
        : |   :         :   | x
        . *-----------------* -
          : x :  15-2x  : x : 

    The room is 15 by 11 feet.
    The border is \,x feet wide.

    The rug is (15-2x) by (12-2x) feet.
    The area of the rug is 108 ft ^2.

    There is our equation! . . . (15-2x)(12-2x) \:=\:108

    This simplifies to: . 2x^2 - 27x + 36 \:=\:0 \quad\Rightarrow\quad (2x-3)(x-12) \:=\:0

    Hence: . x \:=\:\frac{3}{2},\;\rlap{///////}x \:=\:12


    The width of the border is 1\frac{1}{2} feet.

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  3. #3
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    Regrind, INC, used typewriters platens. The variable cost to regrind each platen is $1.40. The total cost to regrind 70 platens is $400. Find the linear cost function to regrind platens. If regrind platens sell for $9.40 each, how many must be reground and sold to break even?
    If x is the initial cost, then x + 70 * 1.40 = 400. Further, let y platens must be reground and sold to break even. Then x + y * 1.40 = y * 9.40.
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  4. #4
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    The answer to the cost funtion is supposedly: c(x)= 1.40x + 302. and then 38 platens sold to break even. I'm not understanding where the 302 is coming from. Wouldnt it be 1.40x+ 400?
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  5. #5
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    The answer to the cost funtion is supposedly: c(x)= 1.40x + 302.
    In this function, 1.40 is the variable cost (per platen) and 302 is the initial cost (I am not sure about terminology). I gave an equation above that allows finding the initial cost. 400 cannot be the initial cost because it is the total cost of 70 platens.
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