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Math Help - Counting Problem

  1. #1
    Junior Member
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    Counting Problem

    You have more than one pair of shoes, more pairs of pants than pairs of shoes, and more shirts than pairs of pants. You notice that you can combine those items to obtain 105 distinct outfits, each consisting of one pair of shoes, one pair of pants, and one shirt. You deduce that you have _______ pairs of shoes, _______ pairs of pants, and _______ shirts.

    I know this is probably easier than it seems, can I get some help.

    Thank you
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  2. #2
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    Hello, thebristolsound!

    You have more than one pair of shoes,
    more pairs of pants than pairs of shoes,
    and more shirts than pairs of pants.
    You notice that you can combine those items to obtain 105 distinct outfits,
    each consisting of one pair of shoes, one pair of pants, and one shirt.

    You deduce that you have ___ pairs of shoes, ___ pairs of pants, and ___ shirts.

    We are told: . 1 \:<\:\text{shoes} \:<\:\text{pants} \:<\:\text{shirts}

    We find that: . 105 \:=\:3\cdot5\cdot7

    Therefore: . \begin{Bmatrix}\text{3 shoes} \\ \text{5 pants} \\ \text{7 shirts} \end{Bmatrix}

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