math

one third of the people in a convention room are seated in three-fourths of the chairs. THe rest of the people in the room decide to stand. If there are 8 empty chairs, how many people are standing?

Please fully explain because i am sooo confused!!!

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  1. let there be p people, c chairs

    There are 8 unused chairs. 3/4 were used, meaning the 8 chairs are 1/4 of all.

    c/4 = 8
    c = 32

    Now,

    p/3 = 3c/4
    p/3 = 96/4 = 24
    p = 72

    check:
    1/3 of 72 = 24
    3/4 of 32 = 24
    8 chairs left over

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  2. One-thirds of the people in a room are seated in three-fourths of the
    chairs. The rest of the people are standing. If there are 6 empty chairs,
    how many people have occupied the chair?

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