document.write( "Question 1209129: If the prize pool is $2000 and I’m in 856th place out of 3,000 people, how much would I receive from the prize pool? \n" ); document.write( "

Algebra.Com's Answer #847726 by ikleyn(52868) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "If the prize pool is $2000 and I’m in 856th place out of 3,000 people,
\n" ); document.write( "how much would I receive from the prize pool?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Generally speaking, the rules of the game / (of the competition) should be established by the problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But since the problem does not establish the rules, I will establish them myself as I like to establish them. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Naturally, I will establish the rules by the most simple way, \r\n" );
document.write( "throwing aside all the details that are unnecessary to me.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In particular, I will assume that the dollar is divisible by any integer number of parts.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, let the rule is dictated by this table \r\n" );
document.write( "\r\n" );
document.write( "             Last                          First\r\n" );
document.write( "\r\n" );
document.write( "     Place   3000  2999  2998  2997  . . .   1\r\n" );
document.write( "\r\n" );
document.write( "     Prize     d    2d    3d    4d   . . . 3000d\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where  \"d\"  is some real number of dollars, not necessary integer number, \r\n" );
document.write( "but, perhaps, any rational number of dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the unique restriction is for the sum\r\n" );
document.write( "\r\n" );
document.write( "    S = d + 2d + 3d + . . . + 3000d = 2000  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It can be written in the form\r\n" );
document.write( "\r\n" );
document.write( "     = 2000,\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    4501500*d = 2000,  d =  =  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the person on the 856 place will get   = 0.953015661 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You may treat it in any way you want.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );