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  • 1 month ago

    50 + 60 + 70 + ... = 950

    Let n be the number of floors.

    40 + 10(1) + 40 + 10(2) + 40 + 10(3) + ... + 40 + 10(n) = 950

    40n + 10(1 + 2 + ... + n) = 950

    ...............n

    40n + 10∑ i = 950

    ..............i=1

    40n + 10(n(n + 1))/2 = 950

    40n + 5n^2 + 5n = 950

    5n^2 + 45n = 950

    n^2 + 9n = 190

    n^2 + 9n - 190 = 0

    (n + 19)(n - 10) = 0

    n = 10 or n = -19

    A negative number of floors makes no sense so discard n = -19, leaving just

    n = 10

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