document.write( "Question 329657: Different amounts are invested at 6%, 7%, and 8% yearly interest. The amount invested at 7% is $300 more than what is invested at 6%, and the total yearly income from all three investments is $208. A total of $2900 is invested. Find the amount invested at each rate. \r
\n" ); document.write( "\n" ); document.write( "THANKS TO ANYONE WHO CAN HELP!!! \n" ); document.write( "
Algebra.Com's Answer #236321 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Different amounts are invested at 6%, 7%, and 8% yearly interest.
\n" ); document.write( " The amount invested at 7% is $300 more than what is invested at 6%,
\n" ); document.write( "and the total yearly income from all three investments is $208.
\n" ); document.write( "A total of $2900 is invested.
\n" ); document.write( "Find the amount invested at each rate.
\n" ); document.write( ":
\n" ); document.write( "Let x = amt invested at 6$
\n" ); document.write( "Let y = amt invested at 7%
\n" ); document.write( "Let z = amt invested at 8%
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"The amount invested at 7% is $300 more than what is invested at 6%,\"
\n" ); document.write( "y = x + 300
\n" ); document.write( ":
\n" ); document.write( "\"the total yearly income from all three investments is $208.\"
\n" ); document.write( ".06x + .07y + .08z = 208
\n" ); document.write( "get rid of the decimals, mult by 100
\n" ); document.write( "6x + 7y + 8z = 20800
\n" ); document.write( "Replace y with (x+300)
\n" ); document.write( "6x + 7(x+300) + 8z = 20800
\n" ); document.write( "6x + 7x + 2100 + 8z = 20800
\n" ); document.write( "13x + 8z = 20800 - 2100
\n" ); document.write( "13x + 8z = 18700
\n" ); document.write( ":
\n" ); document.write( "\"A total of $2900 is invested.\"
\n" ); document.write( "x + y + z = 2900
\n" ); document.write( "Replace y with (x+300)
\n" ); document.write( "x + (x+300) + z = 2900
\n" ); document.write( "2x + z = 2900 - 300
\n" ); document.write( "2x + z = 2600
\n" ); document.write( ":
\n" ); document.write( "Two equation two unknowns, use elimination here,
\n" ); document.write( "mult the above equation by 8, subtract: 13x + 8z = 18700
\n" ); document.write( "16x + 8z = 20800
\n" ); document.write( "13x + 8z = 18700
\n" ); document.write( "------------------subtraction eliminates z, find x
\n" ); document.write( "3x = 2100
\n" ); document.write( "x = \"2100%2F3\"
\n" ); document.write( "x = $700 invested at 6%
\n" ); document.write( ":
\n" ); document.write( "Find y using, y = x + 300
\n" ); document.write( "y = 700 + 300
\n" ); document.write( "y =$1000 invested at 7%
\n" ); document.write( ":
\n" ); document.write( "Find z using, x + y + z = 2900
\n" ); document.write( "700 + 1000 + z = 2900
\n" ); document.write( "z = 2900 - 1700
\n" ); document.write( "z = $1200 invested at 8%
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check the solution by finding the total interest
\n" ); document.write( ".06(700) + .07(1000) + .08(1200) =
\n" ); document.write( "42 + 70 + 96 = 208; confirms our solutions of x=700, y=100, z=1200\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );