document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176551>Question 176551</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pat's present age is three-fourths of Ken's present age. In 15 years the sum of their ages will be 58, Find their present ages. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131724 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=131724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = pat's present age.<BR>\n" );
document.write( "let y = ken's present age.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Pat's present age is three-fourths of Ken's present age.<BR>\n" );
document.write( "x = 3/4 * y<BR>\n" );
document.write( "---<BR>\n" );
document.write( "In 15 years the sum of their ages will be 58<BR>\n" );
document.write( "x + 15 + y + 15 = 58<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "x + y + 30 = 58<BR>\n" );
document.write( "subtract 30 from both sides of equation to get:<BR>\n" );
document.write( "x + y = 28<BR>\n" );
document.write( "---<BR>\n" );
document.write( "substitute 3/4 * y for x to get:<BR>\n" );
document.write( "3/4 * y + y = 28<BR>\n" );
document.write( "multiply both sides of equation by 4 to get:<BR>\n" );
document.write( "3*y + 4*y = 4*28<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "7*y = 4*28<BR>\n" );
document.write( "divide both sides of equation by 7 to get:<BR>\n" );
document.write( "y = 4*28/7<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = 16<BR>\n" );
document.write( "---<BR>\n" );
document.write( "since x = 3/4*y, then:<BR>\n" );
document.write( "x = (3/4)*16 = 3*16/4 = 3*4 = 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "x = 12<BR>\n" );
document.write( "y = 16<BR>\n" );
document.write( "---<BR>\n" );
document.write( "pat is 12<BR>\n" );
document.write( "ken is 16<BR>\n" );
document.write( "pat's age is 3/4 * ken's age.<BR>\n" );
document.write( "in 15 years, pat will be 27 and ken will be 31.<BR>\n" );
document.write( "sum of their ages will be 58<BR>\n" );
document.write( "everything checks out.<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "pat is 12<BR>\n" );
document.write( "ken is 16<BR>\n" );
document.write( "--- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );