math

how many envelopes can be made out of a sheet of paper 3m 24cm by 1m 72cm,if each envelope requires a piece of paper of side 18cm by 12cm?

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  1. the sheet of paper is
    324 cm by 172 cm
    The tempation is to say:
    area of whole paper = 55728 cm^2
    area of 1 envelope = 216
    so we have 55728/216 or 258 envelopes.
    BUT, not so fast .....

    If we lay the length of the envelope along the long side of the large sheet, we can get 324/18 or 18 along that side
    the number of envelopes along the short side is 172/12 = 14 1/3
    but we need whole numbers,
    so number of envelopes = 18x14 or 252
    with some waste of paper.

    If we lay the width of the envelope along the long side of the large sheet, we can get 324/12 or 27 of them, but then along the other side we would get 172/18 or 9.55..
    Again we could only get 9 rows, for a number of envelopes of 27x9 = 243

    The largest number of envelopes is 252

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