document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144613>Question 144613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105379 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=105379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Jane invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. She received yearly interest of $130. Randy also invested in the same scheme, but he interchanged the amounts invested, and received $4 more as interest. How much amount did each of them invest at different rates?<BR>\n" );
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document.write( "Let x = amt J invested at 12%<BR>\n" );
document.write( "Let y = amt J invested at 10%<BR>\n" );
document.write( "J's total interest = $130<BR>\n" );
document.write( "Also<BR>\n" );
document.write( "x = amt R invested at 10%<BR>\n" );
document.write( "y = amt R invested at 12%<BR>\n" );
document.write( "R's total interest = $134<BR>\n" );
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document.write( "Two equations<BR>\n" );
document.write( ".12x + .10y = 130 (J's investments)<BR>\n" );
document.write( ".10x + .12y = 134 (R's investments)<BR>\n" );
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document.write( "Multiply the 1st equation by 1.2 and subtract the 2nd equation, find x<BR>\n" );
document.write( ".144x + .12y = 156<BR>\n" );
document.write( ".10x  + .12y = 134<BR>\n" );
document.write( "---------------------subtracting eliminates y<BR>\n" );
document.write( ".044x = 22<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22%2F.044 ALIGN=MIDDLE  ALT=\"22%2F.044\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = $500; J has invested at 12% and R has invested at 10%<BR>\n" );
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document.write( "Find y using (.12x + .10y = 130)<BR>\n" );
document.write( ".12(500) + .10y = 130<BR>\n" );
document.write( "60 = .10y = 130<BR>\n" );
document.write( ".10y = 130 - 60<BR>\n" );
document.write( ".1y = 70<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F.1 ALIGN=MIDDLE  ALT=\"70%2F.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = $700; J has invested at 10% and R has invested at 12%<BR>\n" );
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document.write( "Check solution using (.10x + .12y = 134)<BR>\n" );
document.write( ".10(500) + .12(700) =<BR>\n" );
document.write( "50 + 84 = 134; confirms our solutions </SPAN>\n" );
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