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Math Help - *URGENT* Linear Equation (Represent 'n' in terms of 'p')

  1. #1
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    *URGENT* Linear Equation (Represent 'n' in terms of 'p')

    Hi, i have a maths assignment i am having trouble with, it is due very soon, and i dont want to lose marks for it. I hope you can help.

    Here is the problem.

    Nella is an artist who loves to decorate terracotta pots. She decides to set up a stall at the local community market selling these. She completes some thorough research before setting up the stall and determines that the relationship between the selling prove and the number of pots sold is linear. Nella estimates that id she sells them for $8, she would sell 50 pots per day, but if the price were increased to $12, she would only sell 25 pots.

    Find a linear equation (i.e. a model) to represent the number of pots sold (n) in terms of the selling price (p) in dollars.
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  2. #2
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    linear equation

    Basically, you have two points on a line (p(1),n(1)) and (p(2),n(2)), and you use these in the linear equation y=mx+b, or in your case, n(p)=mp+b. First, you must notice that the question asks for n in terms of p, take out the middle words, and you have n of p, or written mathematically n(p). This is why I have set up p as the first coordinate in the ordered pair, it is independent, n depends on it. Now, you can either use point-slope form
    y-y(1)=m(x-x(1)) (or for this p-p(1)=m(n-n(1)))
    or you can use slope-intercept
    y=mx+b
    (which for some reason is easier to remember but mathematically it takes longer to solve). First, you must find the slope:
    m=(p(2)-p(1))/(n(2)-n(1))=(25-50)/(12-8)

    Then solve the equation
    p-50=(-25/4)(n-8) or
    p-25=(-25/4)(n-12)
    for p (either one you use, you will come up with the same answer). Or you can solve
    50=(-25/4)(8)+b
    for b and plug it back into n(p)=mp+b, and again you should get the same answer which is:
    n(p)=(-25/4)p+100.

    Try solving both ways, just for practice. To check your answer, plug either point back in and make sure you have equality. That's the great thing about math, you know when you're right!!

    Have Fun,
    jsmath22
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