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10 August, 03:00

A company makes greeting cards and their research shows that that price and demand are related linearly: p=mx + b. They know that for every additional card they wish to sell they need to drop the price by $0.05. They also know that in order to sell 300 cards they need to set the price at $7. Find the linear equation relating P price to demand. Preview p =

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  1. 10 August, 03:19
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    p = - 0.05m + 22

    Step-by-step explanation:

    As given in question,

    The relation between the price and demand can be given by,

    p=mx + b

    where is p is price and x is demand.

    Since in order to sell 300 cards the price has to be fix at $7.

    So,

    7 = 300m+b (1)

    And for every additional card they need to drop the price by $0.05.

    So,

    7-0.05 = 301m+b

    =>6.95 = 301m + b (2)

    Subtracting equation (1) from equation (2), we will have

    6.95 - 7 = 301m - 300m

    =>m = - 0.05

    By putting the value of m in equation (1), we get

    7 = 300. (-0.05) + b

    => b = 22

    So, the linear equation that show the relation between price and demand is given by

    p = - 0.05m + 22
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