document.write( "Question 1188035: Cindy, Derrick and Edmund had $410 altogether. Cindy gave 1/3 of her money to
\n" ); document.write( "Edmund, Derrick then gave 2/5 of his money to Cindy. As a result, Derrick had $20
\n" ); document.write( "less than Cindy and $30 less than Edmund. How much money did Cindy have at
\n" ); document.write( "first? \n" ); document.write( "

Algebra.Com's Answer #819094 by ikleyn(52817) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Cindy, Derrick and Edmund had $410 altogether. Cindy gave 1/3 of her money to
\n" ); document.write( "Edmund, Derrick then gave 2/5 of his money to Cindy. As a result, Derrick had $20
\n" ); document.write( "less than Cindy and $30 less than Edmund. How much money did Cindy have at first?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Let solve the problem in a backward manner.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be what Derrick had finally.\r\n" );
document.write( "\r\n" );
document.write( "Then Cindy had (x+20) dollars at the end;  Edmund had (x+30) dollars at the end.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The total is $410;  it did not change after these interior changes.  So\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x + (x+20) + (x+30) = 410\r\n" );
document.write( "\r\n" );
document.write( "           3x + 50 = 410\r\n" );
document.write( "\r\n" );
document.write( "           3x = 410 - 50 = 360\r\n" );
document.write( "\r\n" );
document.write( "            x = 360/3 = 120  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus at final, Derrick had  120 dollars;  Cindy had 120+20 = 140 dollars  and  Edmund had 120+30 = 150 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we will make one step back, from the end to the beginning.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    As the problem says, Derrick gave 2/5 of his money to Cindy.\r\n" );
document.write( "\r\n" );
document.write( "    Hence, Derrick left with only 3/5 of his money, and this 3/5 of his original money is 120 dollars.\r\n" );
document.write( "\r\n" );
document.write( "    It means that originally Derrick had   = 5*40 = 200 dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       HENCE, Derrick gave  2/5  of $200,  or 80 dollars to Cindy.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   \r\n" );
document.write( "    The problem says: \"Cindy gave 1/3 of her money to Edmund\".\r\n" );
document.write( "\r\n" );
document.write( "    So, Cindy left with 2/3 of her original money, PLUS 80 dollars she got from Derrick.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    So, we write this equation  for the Cindy original amount \"C\"\r\n" );
document.write( "\r\n" );
document.write( "         = 140  dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    We solve this equation easily and get   = 140-80 = 60;  hence  C =  = 90.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Cindy had 90 dollars, at first.\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( "Solving backward allows to untangle the problem and obtain the solution in a simple manner.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );