document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174786>Question 174786</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A woman invested P25,000 in two business ventures, last year she made a profit of 15% from the first venture but lost 5% from the second venture. if the last years income from the two investments was equivalent to a return of 8% of the entire amount invested, how much had she invested in each venture? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129858 by </B><A HREF=/tutors/aboutme.mpl?userid=actuary><B>actuary(112)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=actuary><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, what are the equations that describe the situation:\r<BR>\n" );
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document.write( "Let x be the amount invested in the first venture.\r<BR>\n" );
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document.write( "Let Y be the amount invested in the second venture.\r<BR>\n" );
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document.write( "So x + y = 25000 (#1) (I'll disregard including the \"P\" for pounds in the intermediate steps of my calculation)\r<BR>\n" );
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document.write( ".15x -.05y = .08*25000 (#2)(This equation describes the relationship between th ereturn on each of the two ventures and the return on the total amount invested.\r<BR>\n" );
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document.write( ".15x - .05 (25000 - x) = 2000 (Substituting for \"y\" based on equation  #1)     performing the multiplication\r<BR>\n" );
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document.write( "Simplify  \r<BR>\n" );
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document.write( ".15x - 1250 +.05x = 2000<BR>\n" );
document.write( "Rearrange the equation\r<BR>\n" );
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document.write( ".2x = 2000+1250 = 3250\r<BR>\n" );
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document.write( "So x = 3250/.2 = P16250\r<BR>\n" );
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document.write( "From equation #1, solve for y\r<BR>\n" );
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document.write( "y = 25000 - 16260 =P8750\r<BR>\n" );
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document.write( "Checking the results by substituting the answers into the equations\r<BR>\n" );
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document.write( "16250 + 8750 = 25000 (OK)\r<BR>\n" );
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document.write( ".15*16250 -.05*8750 = 2437.5 - 437.5 = 2000\r<BR>\n" );
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document.write( "25000*.08 = 2000 (OK) </SPAN>\n" );
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