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Math Help - Price/Cost Problem

  1. #1
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    Price/Cost Problem

    A certain bakery ran a promotion: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x?

    A 15
    B 18
    C 21
    D 25
    E 30
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  2. #2
    Member
    Joined
    Jun 2009
    Posts
    83

    Re: Price/Cost Problem

    Found the answer:

    P1 is the normal price.
    P2 is the promotion price.

    X*P1=15 : X purchased at the normal price for $15
    (X+3)*P2 = 15 : But you get 3 more, so X+3 times whatever the promotion price is also $15

    Now deal with those dozen. A dozen purchased at the promotion price (P2) is $2 less than a dozen purchased at the normal price (P1):

    12P1 - 2 = 12P2

    Three equations, three unknowns. Solve it with algebra, or substitute in the different answers to check if they work.

    In each case use the given x to solve two of the equations, then check those values in the third equation.

    If x=15

    (x+3)*P2 = 15 substitute 18P2 = 15 divide P2 = 5/6

    12P1 - 2 = 12P2 substitute and add 2 to both sides 12P1 = 10+2 = 12 so P1 = 1

    Check with the third equation x*P1=15 substitute 15*1=15

    This is the correct answer.

    Try the others just for fun.
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