document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175232>Question 175232</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073048314/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I can't figure out the following equation:\r<BR>\n" );
document.write( "\n" );
document.write( "Paul jogged half as many miles (mi) as Lucy and 7 less than Isaac. If the three ran a total of 23 MI, how far did each person run? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130317 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=130317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of miles paul jogged.<BR>\n" );
document.write( "let y = number of miles lucy jogged.<BR>\n" );
document.write( "let z = number of miles isaac jogged.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "paul jogged half as many miles as lucy:<BR>\n" );
document.write( "x = .5y<BR>\n" );
document.write( "solving for y, we get:<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "paul jogged 7 miles less than isaac.<BR>\n" );
document.write( "x = z-7<BR>\n" );
document.write( "solving for z, we get:<BR>\n" );
document.write( "z = x+7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the total number of miles jogged is 23:<BR>\n" );
document.write( "x + y + z = 23<BR>\n" );
document.write( "---<BR>\n" );
document.write( "we can substitute 2x for y, and x+7 for z to get:<BR>\n" );
document.write( "x + 2x + x + 7 = 23<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "4x + 7 = 23<BR>\n" );
document.write( "subtract 7 from both sides to get:<BR>\n" );
document.write( "4x = 23 - 7 = 16<BR>\n" );
document.write( "divide both sides by 4 to get:<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now that we have x = 4, we can go back to the original equation and find the value of y and z.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "paul jogged 4 miles (x = number of miles paul jogged).<BR>\n" );
document.write( "this means that lucy must have jogged 8 (y = 8) because 4 is 1/2 of 8.<BR>\n" );
document.write( "this means that isaac must have jogged 11 (z = 11) because 4 is 11 minus 7.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "x + y + z = 23<BR>\n" );
document.write( "substituting, we get:<BR>\n" );
document.write( "4 + 8 + 11 = 23<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "23 = 23 proving the values for x,y,z are good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "paul jogged 4 miles.<BR>\n" );
document.write( "lucy jogged 8 miles.<BR>\n" );
document.write( "isaac jogged 11 miles.<BR>\n" );
document.write( "--- </SPAN>\n" );
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