document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206158>Question 1206158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "A football team played 38 games for a total of 70 points. 3 points for a win 1 point for a draw, no points for lost games. The team won twice as many games as they drew. How many games were lost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843406 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "An informal solution (good mental exercise!!)....<br><BR>\n" );
document.write( "They won twice as many games as they drew.<BR>\n" );
document.write( "For each \"group\" of two wins and one draw, they earned 2(3)+1(1) = 6+1 = 7 points.<BR>\n" );
document.write( "All together, they earned 70 points; the number of those \"groups\" must have been 70/7 = 10.<BR>\n" );
document.write( "So they must have won 10*2 = 20 games and drawn 10*1 = 10 games.<BR>\n" );
document.write( "That's a total of 20+10 = 30 games in which they earned points.<BR>\n" );
document.write( "Since the total number games was 38, the number of games they lost was 38-30 = 8.<br><BR>\n" );
document.write( "ANSWER: 8<br><BR>\n" );
document.write( "The EXACT same solution, formally....<br><BR>\n" );
document.write( "let x = # of games they drew<BR>\n" );
document.write( "then 2x = # of games they won<br><BR>\n" );
document.write( "At 3 points for each win and 1 point for each draw (and 0 points for each loss), they earned a total of 70 points:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%283%29%2Bx%281%29=70 ALIGN=MIDDLE  ALT=\"2x%283%29%2Bx%281%29=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2Bx=70 ALIGN=MIDDLE  ALT=\"6x%2Bx=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=70 ALIGN=MIDDLE  ALT=\"7x=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=70%2F7=10 ALIGN=MIDDLE  ALT=\"x=70%2F7=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "# of games won: 2x = 2(10) = 20<BR>\n" );
document.write( "# of games drawn: x = 10<BR>\n" );
document.write( "# of games in which they earned points: 20+10 = 30<BR>\n" );
document.write( "# of games they lost: 38-30 = 8<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );