document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=363118>Question 363118</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	<BR>\n" );
document.write( "I am four times older than my sister was when she was half as young as I was. In 15 years our combined ages will be 100. How old are we now?\r<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Let x = your age<BR>\n" );
document.write( "    y = your sister's age<BR>\n" );
document.write( "    n = no. of years ago when your sister was half as young as you were\r<BR>\n" );
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document.write( "Equation 1: <BR>\n" );
document.write( "    x = 4(y-n)\r<BR>\n" );
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document.write( "Equation 2:<BR>\n" );
document.write( "    y-n   = (x-n)/2<BR>\n" );
document.write( "    2y-2n = x-n<BR>\n" );
document.write( "        n = 2y-x\r<BR>\n" );
document.write( "\n" );
document.write( "Equation 3:<BR>\n" );
document.write( "     x+15+y+15 = 100<BR>\n" );
document.write( "          x+y  = 70\r<BR>\n" );
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document.write( "Substituting the n = 2y-x in Equation 1<BR>\n" );
document.write( "            x = 4(y-n)<BR>\n" );
document.write( "              = 4[y-(2y-x)]<BR>\n" );
document.write( "              = 4(y-2y+x)<BR>\n" );
document.write( "              = -4y + 4x<BR>\n" );
document.write( "              = 4y/3\r<BR>\n" );
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document.write( "Substituting x = 4y/3 in Equation 3<BR>\n" );
document.write( "           x+y = 70<BR>\n" );
document.write( "         4y/3+y= 70<BR>\n" );
document.write( "      3[4y/3+y = 70] <BR>\n" );
document.write( "        4y+3y  = 210<BR>\n" );
document.write( "            7y = 210<BR>\n" );
document.write( "             y = 30       Your sister's age now is 30 yrs old<BR>\n" );
document.write( "             x = 4/3(30)<BR>\n" );
document.write( "               = 40       Your age now is 40 yrs old<BR>\n" );
document.write( "              </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258878 by </B><A HREF=/tutors/aboutme.mpl?userid=amoresroy><B>amoresroy(361)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amoresroy><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=amoresroy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "	\r<BR>\n" );
document.write( "\n" );
document.write( "Solution:<BR>\n" );
document.write( "Let x = your age<BR>\n" );
document.write( "    y = your sister's age<BR>\n" );
document.write( "    n = no. of years ago when your sister was half as young as you were\r<BR>\n" );
document.write( "\n" );
document.write( "Equation 1: <BR>\n" );
document.write( "    x = 4(y-n)\r<BR>\n" );
document.write( "\n" );
document.write( "Equation 2:<BR>\n" );
document.write( "    y-n   = (x-n)/2<BR>\n" );
document.write( "    2y-2n = x-n<BR>\n" );
document.write( "        n = 2y-x\r<BR>\n" );
document.write( "\n" );
document.write( "Equation 3:<BR>\n" );
document.write( "     x+15+y+15 = 100<BR>\n" );
document.write( "          x+y  = 70\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting the n = 2y-x in Equation 1<BR>\n" );
document.write( "            x = 4(y-n)<BR>\n" );
document.write( "              = 4[y-(2y-x)]<BR>\n" );
document.write( "              = 4(y-2y+x)<BR>\n" );
document.write( "              = -4y + 4x<BR>\n" );
document.write( "              = 4y/3\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting x = 4y/3 in Equation 3<BR>\n" );
document.write( "           x+y = 70<BR>\n" );
document.write( "         4y/3+y= 70<BR>\n" );
document.write( "      3[4y/3+y = 70] <BR>\n" );
document.write( "        4y+3y  = 210<BR>\n" );
document.write( "            7y = 210<BR>\n" );
document.write( "             y = 30       <BR>\n" );
document.write( "             Your sister's age now is 30 yrs old<BR>\n" );
document.write( "             x = 4/3(30)<BR>\n" );
document.write( "               = 40       <BR>\n" );
document.write( "             Your age now is 40 yrs old<BR>\n" );
document.write( "              </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );