document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159069>Question 159069</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395352495/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 2 years ago Paul was 7 times as old as Matt. 2 years from now, Paul will be 5 times as old is Matt. How old are Paul and Matt?  I do have the answer, but can't come up  with the correct equation.\r<BR>\n" );
document.write( "\n" );
document.write( "TIA </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117167 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=117167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let P = paul's age now.<BR>\n" );
document.write( "let M = Matt's age now.<BR>\n" );
document.write( "2 years ago Paul was 7 times as old as Matt (was then is implied but not stated).<BR>\n" );
document.write( "2 years ago Paul will be 5 times as old as Matt (will be then is implied but not stated).<BR>\n" );
document.write( "equations become<BR>\n" );
document.write( "P-2 = 7*(M-2) = 7*M - 14<BR>\n" );
document.write( "P+2 = 5*(M+2) = 5*M + 10<BR>\n" );
document.write( "adding 2 to both sides of the first equation and subtracting 2 from both sides of the second equation and they become<BR>\n" );
document.write( "P = 7*M - 14 + 2 = 7*M - 12<BR>\n" );
document.write( "P = 5*M + 10 - 2 = 5*M + 8<BR>\n" );
document.write( "since they both equal the same thing they are equal to each other so they become<BR>\n" );
document.write( "7*M - 12 = 5*M + 8<BR>\n" );
document.write( "solving for M, equation becomes<BR>\n" );
document.write( "2*M = 20<BR>\n" );
document.write( "M = 10<BR>\n" );
document.write( "substituting for M in the first equation gets<BR>\n" );
document.write( "P = 7*M - 12<BR>\n" );
document.write( "P = 7*10 - 12<BR>\n" );
document.write( "P = 70 - 12<BR>\n" );
document.write( "P = 58<BR>\n" );
document.write( "substituting for P and M in the second equation gets<BR>\n" );
document.write( "P = 5*M + 8<BR>\n" );
document.write( "58 = 5*10 + 8<BR>\n" );
document.write( "58 = 58<BR>\n" );
document.write( "values for P and M are good.<BR>\n" );
document.write( "answer is<BR>\n" );
document.write( "P = 58<BR>\n" );
document.write( "M = 10 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );