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Math Help - Linear Equation Worded Problem

  1. #1
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    Linear Equation Worded Problem

    The cost, $C, of manufacturing each jacket of a particular type is given by the formula

    C = an + b for 0 < n ≤ 300

    where a and b are constants and n is the size of the production run of this type of jacket.

    For making 100 jackets, the cost is $108 each.
    For making 120 jackets, the cost is $100 each.

    a) Find the values of a and b.
    b) Sketch the graph of C against n for 0 < n ≤ 300.
    c) Find the cost of manufacturing each jacket if 200 jackets are made.
    d) If the cost of manufacturing each jacket is $48.80, find the size of the production run.

    If someone could point me in the right direction it would be much appreciated.
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  2. #2
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    Re: Linear Equation Worded Problem

    Hey Fratricide.

    Please show us what you have tried and what you have thought about to solve the problem.
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  3. #3
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    Re: Linear Equation Worded Problem

    Initially I thought that I could substitute some values, so I did 108 = 100a + b and tried solving for a and b but got hideously incorrect answers, and from there I have come to you.
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  4. #4
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    Re: Linear Equation Worded Problem

    Make the other equation for production of 120 jackets and get the values for a and b. thereafter everything will fall in its place.
    Thanks from Fratricide
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  5. #5
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    Re: Linear Equation Worded Problem

    Not quite sure I understand what you mean?
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  6. #6
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    Re: Linear Equation Worded Problem

    108 = 100a + b
    100 = 120a + b
    This will give a = -2/5 and b = 148
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  7. #7
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    Re: Linear Equation Worded Problem

    Thanks for your help. From there I was able to finish the question... mostly. The part of the question asking me to sketch the graph has me stumped. I thought I knew what I was doing, but then a wild 28 appeared!
    Where does the 28 come from?
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  8. #8
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    Re: Linear Equation Worded Problem

    Bump!
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  9. #9
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    Re: Linear Equation Worded Problem

    What appears to me is that he has just rtaken the production size to be 300 for the purpose of graph, though we can draw the graph in the absence of the point ( 300 , 28 )
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