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Suppose a market research company finds that at a price of p=$25,they would sell x=56 tiles each month. If they lower the price to p=$20, then more people would purchase the tile, and they can expect to sell x=66 tiles in a month's time. Find the equation of the line for the demand equation. Writ answer in the form p=mx+b

  • algebra -

    for this problem, we will substitute the given to the equation p = mx + b, and then we solve simultaneously (two equations, two unknowns):
    25 = 56m + b
    20 = 66m + b
    to solve this, we can multiply one equation by -1 so that if we add the equations, the b will be cancelled:
    -25 = -56m - b
    20 = 66m + b
    -5 = 10m

    m = -1/2
    to get be, we substitute this m to either equations. In this case, let's just substitute to the first equation:
    25 = 56m + b
    25 = 56(-1/2) + b
    25 = -28 + b
    b = 53

    therefore, the equation is
    p = (-1/2)x + 53

    hope this helps~ :)

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