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Math Help - Demand Equation Question

  1. #1
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    Demand Equation Question

    Suppose that 10,000 units of a certain item are sold per day by the entire industry at a price of $150 per item, and that 8000 units can be sold per day by the same industry at a price of $200 per item. Find the demand equation for in terms of , the number of units sold, assuming the demand curve to be a straight line.

    I know the answer will be a straight line, so P(x)=ax+b

    and I know

    if you sell 10000 units, price becomes $150 so in price equation above you get 150=a(10000)+b

    and

    if you sell 8000 units, price becomes $200 so the equation becomes 200=a(8000)+b

    I just can't figure out how to solve to get A and B pretty much...
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by redraider717 View Post
    Suppose that 10,000 units of a certain item are sold per day by the entire industry at a price of $150 per item, and that 8000 units can be sold per day by the same industry at a price of $200 per item. Find the demand equation for in terms of , the number of units sold, assuming the demand curve to be a straight line.

    I know the answer will be a straight line, so P(x)=ax+b

    and I know

    if you sell 10000 units, price becomes $150 so in price equation above you get 150=a(10000)+b

    and

    if you sell 8000 units, price becomes $200 so the equation becomes 200=a(8000)+b

    I just can't figure out how to solve to get A and B pretty much...
    these are simultaneous equations

    150 = 10000a + b ..................(1)
    200 = 8000a + b ....................(2)

    \Rightarrow -50 = 2000a ....................(1) - (2)

    now solve for a. when finished, plug the value you got for a into either of the original equations to solve for b
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