document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054184>Question 1054184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the price of two house is 16:23.two years later the price of the first had raised by 10% and that of the second by $477.the ratio of the price became 11:20.find the original prices of the houses. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669381 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=669381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a equal the price of the first home.<BR>\n" );
document.write( "let b equal the price of the second home.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the ratio of the price of the first home to the price of the second home is equal to 16/23.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that the price of the first home divided by the price of the second home is equal to 16/23.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a/b = 16/23\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 2 years the price of the first home has increased to 1.1 times its original amount.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 2 years the price of the second home has increased by 477 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 2 years, the ratio of the first home to the price of the second home is equal to 11/20.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that the price of the first home divided by the price of the second home has become 11/20.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1.1 * a) / (b + 477) = 11/20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a/b = 16/23\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1.1 * a) / (b + 477) = 11/20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the first equation, solve for a to get a = 16/23 * b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the second equation, replace a with 16/23 * b to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(1.1 * 16/23 * b) / (b + 477) = 11 / 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "17.6 / 23 * b / (b + 477) = 11 / 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by 20 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "352 / 23 * b / (b + 477) = 11\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by 23 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "352 * b / (b + 477) = 253\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by (b + 477) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "352 * b = 253 * (b + 477)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "352 * b = 253 * b + 120681\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 253 * b from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "352 * b - 253 * b = 120681\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "99 * b = 120681\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 99 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b = 120681 / 99 = 1219\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you know that a = 16/23 * b, this means that a = 848.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the price of the first home is currently 848.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the price of the second home is currently 1219\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the ratio of the first home to the second home is 848 / 1219 = 16/23\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in 2 years, the price of the first home will be 848 * 1.1 = 932.8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in 2 years, the price of the second home will be 1219 + 477 = 1696.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in 2 years, the ratio of the price of the first home to the price of the second home will be 932.8 / 1696 = 11/20.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "numbers look good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the price of the first home is currently 848.<BR>\n" );
document.write( "the price of the second home is currently 1219.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );