document.write( "Question 1184472: Natalie, Rachel and Winnie were given a box of beads. Natalie took 5/9 of the beads and then put 14 beads back. Rachel took 1/5 of the remaining beads and then put 8 beads back. Winnie then took half of the remaining beads. The rest of the beads in the box were packed equally into 12 bags. There were 26 beads in each bag. How many beads were given to the girls? \n" ); document.write( "

Algebra.Com's Answer #815068 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Natalie, Rachel and Winnie were given a box of beads.
\n" ); document.write( "Natalie took 5/9 of the beads and then put 14 beads back.
\n" ); document.write( "Rachel took 1/5 of the remaining beads and then put 8 beads back.
\n" ); document.write( "Winnie then took half of the remaining beads.
\n" ); document.write( "The rest of the beads in the box were packed equally into 12 bags.
\n" ); document.write( "There were 26 beads in each bag. How many beads were given to the girls?
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            There was an error in my previous solution version.\r
\n" ); document.write( "\n" ); document.write( "            Thanks to other solvers who noticed it.\r
\n" ); document.write( "\n" ); document.write( "            I corrected everything, and now you see a corrected version below.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "To make the solution totally clear, I will present the problem's description in steps.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (1)  Natalie took 5/9 of the beads.\r\n" );
document.write( "\r\n" );
document.write( "    (2)  then Natalie returned 14 beads back.\r\n" );
document.write( "\r\n" );
document.write( "    (3)  then Rachel took 1/5 of the remaining beads\r\n" );
document.write( "\r\n" );
document.write( "    (4)  then Rachel returned 8 beads back\r\n" );
document.write( "\r\n" );
document.write( "    (5)  then Winnie took half of the remaining beads.\r\n" );
document.write( "\r\n" );
document.write( "    (6)  then the rest beads were packed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "OK, very good.     It will help    and    very much,  as you will see from what follows.\r\n" );
document.write( "\r\n" );
document.write( "Now I will solve the problem moving backward.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The number of the packed beads is 12*26 = 312.\r\n" );
document.write( "\r\n" );
document.write( "    Hence, the number of beads immediately before step  5  was  312*2 = 624.\r\n" );
document.write( "\r\n" );
document.write( "           the number of beads immediately before step  4  was  624 - 8 = 616.\r\n" );
document.write( "\r\n" );
document.write( "           the number of beads immediately before step  3  was   = 770.   <<<---=== use equation  = 616.\r\n" );
document.write( "\r\n" );
document.write( "           the number of beads immediately before step  2  was  770-14 = 756.\r\n" );
document.write( "\r\n" );
document.write( "           the number of beads immediately before step  1  was   = 1701.  <<<---=== use equation  = 756.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the number of beads, which was given to girls was 1701.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved ( in a backward manner ) .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "///////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I am happy to have so attentive readers (!)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );