Alfonse cuts half a rectangular lawn, 50m by 20m, by mowing strips of equal width around the perimeter. Bart cuts the small rectangle in the middle that's left. How wide a strip does Alfonse cut so that they share the work equally?

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  1. 50 * 20 = 1000

    strip width = s

    interior dimensions

    (50-2s)(20-2s) = half original = 500

    1000 - 140 s + 4 s^2 = 500
    4 s^2 - 140 s +500 = 0

    s^2 - 35 s + 125 = 0

    s = [35 +/- sqrt (1225-500) ]/2
    s = [35+/- 26.92 ] /2
    s = 30.96 or 4.04
    must be 4.04 because strips of 31 each end will not work
    50 - 2(4.04) =41.92
    20 - 2(4.04) = 11.92
    11.92 * 41.92 = 499.6 fine

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  2. gustave is a really demanding student who finishes his work in half the time of other students if he isnt kept busy he takes off his shoes and dances on the desks. His teach assigns him to add the first 5000 odd numbers. come up with the answer and illustrate how gustave can do this fast and get back to his dancing.

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