document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174226>Question 174226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac.  If the three ran a total of 23 miles, how far did each of them run? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129156 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=129156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 miles, how far did each of them run?<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "p = (1/2) L<BR>\n" );
document.write( "p = I - 7<BR>\n" );
document.write( "p + I + L = 23<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "p + 0 - (1/2)L = 0<BR>\n" );
document.write( "p - I +   0    = -7<BR>\n" );
document.write( "p + I +   L    = 23<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Solve the system by any means you know to get:<BR>\n" );
document.write( "p = 4 miles<BR>\n" );
document.write( "I = 11 miles<BR>\n" );
document.write( "L = 8 miles<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "Another way to find the solution:<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "p = (1/2) L<BR>\n" );
document.write( "p = I - 7<BR>\n" );
document.write( "p + I + L = 23<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Rearrange to get:<BR>\n" );
document.write( "L = 2p<BR>\n" );
document.write( "I = p+7<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "p = (1/2) L<BR>\n" );
document.write( "p = I - 7<BR>\n" );
document.write( "p + I + L = 23<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute into p + I + L = 23 to get:<BR>\n" );
document.write( "p + p+7 + 2p = 23<BR>\n" );
document.write( "4x + 7 = 23<BR>\n" );
document.write( "4x = 16<BR>\n" );
document.write( "p = 4 miles (paul)<BR>\n" );
document.write( "L= 2p = 8 miles (Lucy)<BR>\n" );
document.write( "I= p + 7 = 4+7 = 11 miles (Isaac)<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );