document.write( "Question 86954: You have $50,000 to invest, you invest some at 5% and the rest at 4%, you earn $2100 in annual interest, how much did you invest at each rate? \n" ); document.write( "

Algebra.Com's Answer #62895 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Interest(I)=Principal(P) times Rate(R) times Time(T) (note: in this problem, T=1 year)\r
\n" ); document.write( "\n" ); document.write( "Let P=amount invested at 5%
\n" ); document.write( "Interest at 5%=P(0.05)(1)=0.05P\r
\n" ); document.write( "\n" ); document.write( "Then 50,000-P=amount invested at 4%
\n" ); document.write( "Interest at 4%=(50,000-P)(0.04)(1)=(0.04)(50,000-P)\r
\n" ); document.write( "\n" ); document.write( "Now we are told that the interest earned at 5%((0.05)(P)) plus the interest earned at 4%((0.04)(50,000-P)) equals $2100. So, our equation to solve is:\r
\n" ); document.write( "\n" ); document.write( "0.05(P)+0.04(50,000-P)=2100 get rid of parens\r
\n" ); document.write( "\n" ); document.write( "0.05P+2000-0.04P=2100 subtract 2000 from each side\r
\n" ); document.write( "\n" ); document.write( "0.05P+2000-2000-0.04P=2100-2000 collect like terms\r
\n" ); document.write( "\n" ); document.write( "0.01P=100 divide both sides by 0.01\r
\n" ); document.write( "\n" ); document.write( "P=$10,000-----------------------------------amount invested at 5%\r
\n" ); document.write( "\n" ); document.write( "50,000-P=50,000-10,000=$40,000--------------amount invested at 4%\r
\n" ); document.write( "\n" ); document.write( "CK\r
\n" ); document.write( "\n" ); document.write( "0.05*10,000+0.04*40,000=2100\r
\n" ); document.write( "\n" ); document.write( "500+1600=2100
\n" ); document.write( "2100=2100\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
\n" ); document.write( " \n" ); document.write( "

\n" );