document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30876>Question 30876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A traffic check counted 390 cars passing a certain spot on one day and 430 cars at the same spot on the second day.  The first day there were 3 times as many cars going east and half as many cars going west on the second day.  What was the total number of east bound cars and the total number of west bound cars for two days? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17641 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=17641\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "Let's call X to the number of cars going EAST on the 1st day and Y to the number of cars going WEST on the 1st day.\r<BR>\n" );
document.write( "\n" );
document.write( "We can use the information given in the problem to form a simple system of equations and find X and Y. We know:\r<BR>\n" );
document.write( "\n" );
document.write( "\"A traffic check counted 390 cars passing a certain spot on one day\"<BR>\n" );
document.write( "This implies that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+Y+=+390 ALIGN=MIDDLE  ALT=\"X+%2B+Y+=+390\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[recall that X and Y are cars in the FIRST day]\r<BR>\n" );
document.write( "\n" );
document.write( "We also know that:<BR>\n" );
document.write( "\"The first day there were 3 times as many cars going east and half as many cars going west on the second day\"<BR>\n" );
document.write( "This implies that the second day there were X/3 cars going east (because the 1st day had 3 times as many cars going east on the 2nd day) and 2Y cars going west (because the on the first day there were half as many cars going west on the 2nd day).\r<BR>\n" );
document.write( "\n" );
document.write( "So the total number of cars in the second day was X/3 + 2Y. We also know that this number is 430. So we get the system:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28X+%2B+Y+=+390%2C%281%2F3%29X+%2B+2Y+=+430 ALIGN=MIDDLE  ALT=\"system%28X+%2B+Y+=+390%2C%281%2F3%29X+%2B+2Y+=+430\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "You can solve this system with your preferred method. Here's the solution using substitution:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+390%2C%0D%0A++++%281%2F3%29%5Cx+%2B+2%5Cy+=+430+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 1*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax+=+390+-+1%2Ay ALIGN=MIDDLE  ALT=\"1%2Ax+=+390+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+390%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+390%2F1+-+1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A%28390%2F1+-+1%2Ay%2F1%29+%2B+2%5Cy+=+430 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A%28390%2F1+-+1%2Ay%2F1%29+%2B+2%5Cy+=+430\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=180. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+390%2F1+-+1%2Ay%2F1 ALIGN=MIDDLE  ALT=\"x+=+390%2F1+-+1%2Ay%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=210.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=210%2C+y=180+%29 ALIGN=MIDDLE  ALT=\"system%28+x=210%2C+y=180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there were 210 cars going east and 180 cars going west in the 1st day, for a total of 390 cars. The second day, there were X/3 = 70 cars going east and 2Y = 360 cars going west, for a total of 430 cars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );