document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164597>Question 164597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul is 3 years younger than his friend Peter. In seven years, the product of their ages will be five more than the product of their ages five years ago. How old are they now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121285 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Paul is 3 years younger than his friend Peter.<BR>\n" );
document.write( "so:<BR>\n" );
document.write( "Let Peter=x and Paul=x-3 <BR>\n" );
document.write( "In seven years, the product of their ages will be five more than the product of their ages five years ago.<BR>\n" );
document.write( "So:<BR>\n" );
document.write( "Peter's age (x) in seven years will be (x+7) and Paul's age in seven years will be [(x-3)+7]. <BR>\n" );
document.write( "The product of their ages at that time will be[(x+7)*(x-3+7)]. <BR>\n" );
document.write( "Peter's age (x) five years ago was (x-5) and Paul's age five years ago was (x-3-5).<BR>\n" );
document.write( "The product of their ages at that time will be[(x-5)*(x-3-5)]. <BR>\n" );
document.write( "The product of their ages in seven years is 5 more than it was five years ago.<BR>\n" );
document.write( "Therefore:<BR>\n" );
document.write( "[x+7)(x-3+7)=(x-5)(x-3-5)+5<BR>\n" );
document.write( "simplify:<BR>\n" );
document.write( "[x+7)(x+4)=(x-5)(x-8)+5<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x^2+4x+7x+28=x^2-8x-5x+40+5<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "x^2+11x+28=x^2-13x+45<BR>\n" );
document.write( "subtract x^2 from both sides<BR>\n" );
document.write( "11x+28=-13x+45<BR>\n" );
document.write( "add 13x to both sides<BR>\n" );
document.write( "24x+28=45<BR>\n" );
document.write( "Subtract 28 from both sides<BR>\n" );
document.write( "24x=17<BR>\n" );
document.write( "divide both sides by 24<BR>\n" );
document.write( "x=17/24 years old<BR>\n" );
document.write( "since Peter=x, Peter is 17/24 years old; however this doesn't make much since. So to convert to months, we will set 17/24 equal to x/12 and solve for x\r<BR>\n" );
document.write( "\n" );
document.write( "cross multiply and 17*12=24x or 204=24x<BR>\n" );
document.write( "divide both sides by 24 and get x=8.5<BR>\n" );
document.write( "Therefore Peter is 8.5 months old and Paul will be born in 27.5 months <BR>\n" );
document.write( "I hope this helps \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );