document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257986>Question 257986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pls provide formula: lucy ran twice as many miles as paul but 3 less than isaac. they ran total of 23 miles. how far did each run? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189851 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break the problem down into its parts\r<BR>\n" );
document.write( "\n" );
document.write( "\"Lucy ran twice as many miles as Paul but 3 less than Isaac. They ran total of 23 miles. How far did each run?\"\r<BR>\n" );
document.write( "\n" );
document.write( "\"Lucy ran\" <BR>\n" );
document.write( "Let L equal the miles Lucy ran\r<BR>\n" );
document.write( "\n" );
document.write( "\"twice as many miles as Paul\"\r<BR>\n" );
document.write( "\n" );
document.write( "Let P equal miles run by Paul<BR>\n" );
document.write( "L=2P\r<BR>\n" );
document.write( "\n" );
document.write( " \"but 3 less than Isaac\"<BR>\n" );
document.write( "Let I equal miles run by Isaac\r<BR>\n" );
document.write( "\n" );
document.write( "L=I-3\r<BR>\n" );
document.write( "\n" );
document.write( "\"They ran total of 23 miles.\" <BR>\n" );
document.write( "L+P+I=23<BR>\n" );
document.write( "So now we have three equation sin three unknowns. That is just what we need.\r<BR>\n" );
document.write( "\n" );
document.write( "L=2P<BR>\n" );
document.write( "L=I-3<BR>\n" );
document.write( "L+P+I=23<BR>\n" );
document.write( "How far did each run?<BR>\n" );
document.write( "So we are asked for the values of L and P and I<BR>\n" );
document.write( "We rearrange the first two equations.<BR>\n" );
document.write( "We have L=2P<BR>\n" );
document.write( "But we want P by itself<BR>\n" );
document.write( "L=2P<BR>\n" );
document.write( "divide both sides by 2<BR>\n" );
document.write( "L/2=P<BR>\n" );
document.write( "now the other one<BR>\n" );
document.write( "L=I-3<BR>\n" );
document.write( "add 3 to both sides<BR>\n" );
document.write( "L+3=I\r<BR>\n" );
document.write( "\n" );
document.write( "so now we have <BR>\n" );
document.write( "P=L/2<BR>\n" );
document.write( "and I=L+3<BR>\n" );
document.write( "and L+P+I=23<BR>\n" );
document.write( "so now we we substitute L+3 for I and L/2 for P<BR>\n" );
document.write( "L+P+I=23<BR>\n" );
document.write( "L+(L/2)+ (L+3)=23<BR>\n" );
document.write( "Let's remove the parentheses<BR>\n" );
document.write( "L+L/2+L+3=23<BR>\n" );
document.write( "Let's combine<BR>\n" );
document.write( "2L+L/2+3=23<BR>\n" );
document.write( "subtract 3 from both sides<BR>\n" );
document.write( "2L+L/2=20<BR>\n" );
document.write( "multiply both sides by 2<BR>\n" );
document.write( "4L+L=40<BR>\n" );
document.write( "combine <BR>\n" );
document.write( "5L=40<BR>\n" );
document.write( "divide both sides by 5<BR>\n" );
document.write( "L=8<BR>\n" );
document.write( "We also want to solve for P and I <BR>\n" );
document.write( "P=L/2=8/2=4<BR>\n" );
document.write( "and I=L+3=*+3=11\r<BR>\n" );
document.write( "\n" );
document.write( "L = 8 miles,   P = 4 miles,   I = 11 miles<BR>\n" );
document.write( "check<BR>\n" );
document.write( "L+P+I=23<BR>\n" );
document.write( "8+4+11=23<BR>\n" );
document.write( "ok\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );