document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=514594>Question 514594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man has 3 sums of money invested, one at 12%, one at 10% and the last at 8%, his total annual income from the three investments is 2100 the first investment yields as much as the other 2 combined, if he could receive 1% more on each investments his annual income would be increased by 202.50. How much is his investments at each rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343580 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=343580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man has 3 sums of money invested, one at 12%, one at 10% and the last at 8%,<BR>\n" );
document.write( " his total annual income from the three investments is 2100<BR>\n" );
document.write( " the first investment yields as much as the other 2 combined, \"<BR>\n" );
document.write( "How much is his investments at each<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ";<BR>\n" );
document.write( "\"A man has 3 sums of money invested, one at 12%, one at 10% and the last at 8%,<BR>\n" );
document.write( " his total annual income from the three investments is 2100\"<BR>\n" );
document.write( ".12x + .10y + .08z = 2100<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"the first investment yields as much as the other 2 combined, \"<BR>\n" );
document.write( ".12x = .10y + .08z<BR>\n" );
document.write( "rewrite this to<BR>\n" );
document.write( ".12x - .10y - .08z = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"if he could receive 1% more on each investments his annual income would be increased by 202.50\"<BR>\n" );
document.write( ".13x + .11y + .09z = 202.50 + 2100<BR>\n" );
document.write( ".13x + .11y + .09z = 2302.50<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add these two equation<BR>\n" );
document.write( ".12x + .10y + .08z = 2100<BR>\n" );
document.write( ".12x - .10y - .08z = 0<BR>\n" );
document.write( "------------------------addition eliminates y and z, find x<BR>\n" );
document.write( ".24x = 2100<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2100%2F.24 ALIGN=MIDDLE  ALT=\"2100%2F.24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = $8,750 invested at 12%<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the return on this amt<BR>\n" );
document.write( ".12(8750) = $1050<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"the first investment yields as much as the other 2 combined, \"<BR>\n" );
document.write( ".10y + .08z = 1050<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"receive 1% more on each investments his annual income would be increased by 202.50\"<BR>\n" );
document.write( ".01(8750) + .01y + .01z = 202.50<BR>\n" );
document.write( "87.50 + .01y + .01z = 202.50<BR>\n" );
document.write( ".01y + .01z = 202.50 - 87.50<BR>\n" );
document.write( ".01y + .01z = 115<BR>\n" );
document.write( "multiply by 10, subtract the previous equation<BR>\n" );
document.write( ".10y + .10z = 1150<BR>\n" );
document.write( ".10y + .08z = 1050<BR>\n" );
document.write( "--------------------subtraction eliminates y, find z<BR>\n" );
document.write( ".02z = 100<BR>\n" );
document.write( "z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F.02 ALIGN=MIDDLE  ALT=\"100%2F.02\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "z = $5000 invested at 8%<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use equation: .01y + .01z = 115, to find y, replace z<BR>\n" );
document.write( ".01y + .01(5000) = 115<BR>\n" );
document.write( ".01y + 50 = 115<BR>\n" );
document.write( ".01y = 115 - 50<BR>\n" );
document.write( ".01y = 65<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65%2F.01 ALIGN=MIDDLE  ALT=\"65%2F.01\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = $6500 invested at 10%<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Summarize: <BR>\n" );
document.write( "x = $8750 invested at 12%<BR>\n" );
document.write( "y = $6500 invested at 10%<BR>\n" );
document.write( "z = $5000 invested at 8%<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the total return using these values<BR>\n" );
document.write( ".12(8750) + .10y(6500)+ .08(5000) =<BR>\n" );
document.write( "1050 + 650 + 400 = 2100, confirms our solutions\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );