SOLUTION: the tickets in a raffle are numbered 1, 2, 3, and so on. The Price of a ticket is the number of cents equal to the number of the ticket. If the raffled article cost $100, what is

I will reformulate the problem to make my reasoning shorter.


They want you find the minimal integer number value  'n' such that

the sum  1 + 2 + 3 + . . . + n  is greater than or equal to 10,000.


Such sum is  ,  so we need the minimal 'n' such that


     >= 10000.



Simplify this inequality


    n*(n+1) >= 20000.    (*)


Take the square root of 20000:   = 141.42.


    +----------------------------------------------------------+
    |   Now I state that your minimum value of  'n'  is  141.  |
    +----------------------------------------------------------+


Let's check the inequality (*).


    (a)  141*142 = 20022.   Good, ok.


    (b)  140*141 = 19740.   Not good.


At this point, the solution is completed by the simplest and the shortest way.


Your ANSWER  is  n = 141.