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math

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A floor-finishing machine uses bars of wax. Once the bar is worn down to 1/2 its original size, it must be replaced with a new bar. Only full-size bars can be put in the machine. The pieces are melted and recycled to make full-size bars. If you buy 24 bars and recycle all the pieces, how many full-size bars can you use? How much wax will be left over? Your goal is to have as little wasted wax as possible.

  • math - ,

    1st cycle:
    equivalent of 12 bars used, 24 half-bars left over
    recycled to make 12 new bars
    2nd cycle:
    equivalent of 6 bars used, 12 half-bars left over
    recycled to make 6 new bars
    3rd cycle:
    equivalent of 3 bars used, 6 half-bars left over
    recycled to make 3 new bars
    4th cycle:
    equivalent of 1.5 bars used, 3 half-bars left over
    recycled to make 1.5 new bars

    since only full-size bars can be used, only one more bar can be used

    total used: 12+6+3+1.5+1 = 23.5
    So 1/2 bar is left over.

  • math - ,

    thanks for your help.

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