Thursday, June 24, 2010

How do you work this out algebraically?

Twenty-five different positive integers add to 2008. What is the largest value that the least of them can have?How do you work this out algebraically?
The largest value of the lowest number would be when all the numbers are in sequence.


x + (x+1) + (x+2) + 鈥?+ (x+23) + (x+24) = 2008


25x + 300 = 2008


25x = 1708


x = 68.32





The largest value of the lowest number is 68.


68 + 69 + 70 + 鈥?+ 91 + 92 = 2000


68 + 69 + 70 + 鈥?+ 91 + 100 = 2008How do you work this out algebraically?
(n + 1)C2 = 2008


n(n + 1) = 4016


n^2 + n = 4016


n^2 + n - 4016 = 0


Looks like you'll need the quadratic formula.

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