document.write( "Question 1198416: An inheritance is split among 5 brothers. The first receives half of the inheritance plus $1. The second receives half of the remainder plus $2. The third receives half of the remainder plus $3. The fourth receives half of the remainder plus $4. The last brother receives $500. What is the total amount of the inheritance? \n" ); document.write( "

Algebra.Com's Answer #832018 by ikleyn(52805) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "An inheritance is split among 5 brothers.
\n" ); document.write( "The first receives half of the inheritance plus $1.
\n" ); document.write( "The second receives half of the remainder plus $2.
\n" ); document.write( "The third receives half of the remainder plus $3.
\n" ); document.write( "The fourth receives half of the remainder plus $4.
\n" ); document.write( "The last brother receives $\"highlight%28highlight%28the_remaining%29%29\"$ $500.
\n" ); document.write( "What is the total amount of the inheritance?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let the brothers be B1,  B2,  B3,  B4,  and  B5.\r\n" );
document.write( "\r\n" );
document.write( "Let  b[0]  be the entire inheritance.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Brother B1 got half of inheritance + $1,  or  b[0]/2 + 1 dollars.  The remainder is  r[1] = b[0]/2 - 1.    (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Brother B2 got half of the remainder r[1] plus $2, or r[1]/2 + 2.  The remainder is  r[2] = r[1]/2 - 2.    (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Brother B3 got half of the remainder r[2] plus $3, or r[2]/2 + 3.  The remainder is  r[3] = r[2]/2 - 3.    (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Brother B4 got half of the remainder r[3] plus $4, or r[3]/2 + 4.  The remainder is  r[4] = r[3]/2 - 4.    (4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "r[4] is what brother B5 got:  r[4] = 500 = r[3]/2 - 4.\r\n" );
document.write( "\r\n" );
document.write( "From it,   we have  r[3]/2 = 500 + 4 = 504,  which gives  r[3] = 2*504 = 1008.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +----------------------------------------------------------------------+\r\n" );
document.write( "    |   Now I will solve equations (3), (2), (1)  in this backward order.  |\r\n" );
document.write( "    +----------------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (3),  we have  r[2]/2 - 3 = r[3] = 1008,  or  r[2]/2 = 1008+3 = 1011,  which gives  r[2] = 2*1011 = 2022.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (2),  we have  r[1]/2 - 2 = r[2] = 2022,  or  r[1]/2 = 2022+2 = 2024,  which gives  r[1] = 2*2024 = 4048.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (1),  we have  b[0]/2 - 1 = r[1] = 4048,  or  b[0]/2 = 4048+1 = 4049,  which gives  b[0] = 2*4049 = 8098.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The whole inheritance was 8098 dollars.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The method which I used is called a \"backward solution method\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On the way forward I establish the equations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On the way back I solve these equations, one after another.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Nice method, isn't it ?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );