document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170973>Question 1170973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the ages for Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old will they be in three years time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795838 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=795838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "E = peter's age right now<BR>\n" );
document.write( "A = paul's age right now<BR>\n" );
document.write( "Ages are in years.<BR>\n" );
document.write( "I went with the second letter of their names since both started with P. Feel free to label your variables however you want.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "\"The sum of their ages is 24\" means E+A = 24. We can solve for E to get E = 24-A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Five years ago, their ages were E-5 and A-5<BR>\n" );
document.write( "The ratio of these past ages was 3:4, which means we can say,<BR>\n" );
document.write( "(peter's age 5 years ago)/(paul's age 5 years ago) = 3/4<BR>\n" );
document.write( "(E-5)/(A-5) = 3/4<BR>\n" );
document.write( "4(E-5) = 3(A-5) .... cross multiply<BR>\n" );
document.write( "4E-20 = 3A-15<BR>\n" );
document.write( "4(24-A)-20 = 3A-15 ... plug in E = 24-A<BR>\n" );
document.write( "96-4A-20 = 3A-15<BR>\n" );
document.write( "76-4A = 3A-15<BR>\n" );
document.write( "76+15 = 3A+4A<BR>\n" );
document.write( "91 = 7A<BR>\n" );
document.write( "7A = 91<BR>\n" );
document.write( "A = 91/7<BR>\n" );
document.write( "A = 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Paul is currently 13 years old. In three years time, he will be 13+3 = 16 years old.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "E = 24-A<BR>\n" );
document.write( "E = 24-13<BR>\n" );
document.write( "E = 11\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Peter is currently 11 years old. In three years time, he will be 11+3 = 14 years old.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answers:<BR>\n" );
document.write( "Peter will be 14 years of age<BR>\n" );
document.write( "Paul will be 16 years of age<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );