document.write( "Question 1147008: A stockbroker has money in three accounts. The interest rates on the three accounts are 7%, 8%, and 9%. If she has twice as much money invested at 8% as she does in 7%, three times as much at 9% as she has at 7%, and the total interest for the year is $200, how much is invested at each rate? \n" ); document.write( "

Algebra.Com's Answer #768289 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let x be the amount, in dollars, invested at 7%.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the amount invested at 8% is 2x dollars,\r\n" );
document.write( "\r\n" );
document.write( "and  the amount invested at 9% is 3x dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then the equation expressing total interest of three accounts is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    0.07x + 0.08(2x) + 0.09*(3x) = 200   dollars.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    0.07x + 0.16x + 0.27x = 200\r\n" );
document.write( "\r\n" );
document.write( "    0.5x = 200\r\n" );
document.write( "\r\n" );
document.write( "    x    =  = 400.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  $400 invested at 7%;  $800 invested at 8%  and  $1200 invested at 9%.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  0.07*400 + 0.08*800 + 0.09*1200 = 200 dollars,  which is PRECISELY correct (!)\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" );