document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223553>Question 223553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference of two numbers is 12.  Two fifths of the greater number is six more than one third of the lesser number. find both numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167128 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference of two numbers is 12.  Two fifths of the greater number is six more than one third of the lesser number. Find both numbers\r<BR>\n" );
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document.write( "Step 1.  Let x be one smaller number\r<BR>\n" );
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document.write( "Step 2. Let y be the larger number.\r<BR>\n" );
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document.write( "Step 3.  Then -x+y=12 since the difference of two numbers is 12.\r<BR>\n" );
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document.write( "Step 4.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2F5=6%2Bx%2F3 ALIGN=MIDDLE  ALT=\"2y%2F5=6%2Bx%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > since two fifths of the greater number is six more than one third of the lesser number\r<BR>\n" );
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document.write( "Multiply by 15 to get rid of the denominators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A2y%2F5=15%2A6%2B15x%2F3 ALIGN=MIDDLE  ALT=\"15%2A2y%2F5=15%2A6%2B15x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y=90%2B5x ALIGN=MIDDLE  ALT=\"6y=90%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 5x from both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%2B6y=90 ALIGN=MIDDLE  ALT=\"-5x%2B6y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  So here's our system of linear equations  From Steps 3 and 4:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By=12 ALIGN=MIDDLE  ALT=\"-x%2By=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5x%2B6y=90 ALIGN=MIDDLE  ALT=\"-5x%2B6y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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+=+12%2C%0D%0A++++-5%5Cx+%2B+6%5Cy+=+90+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++-1%5Cx+%2B+1%5Cy+=+12%2C%0D%0A++++-5%5Cx+%2B+6%5Cy+=+90+%29%0D%0A++\"   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+=+12+-+1%2Ay ALIGN=MIDDLE  ALT=\"-1%2Ax+=+12+-+1%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12%2F-1+-+1%2Ay%2F-1 ALIGN=MIDDLE  ALT=\"x+=+12%2F-1+-+1%2Ay%2F-1\"   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=-5%2A%2812%2F-1+-+1%2Ay%2F-1%29+%2B+6%5Cy+=+90 ALIGN=MIDDLE  ALT=\"-5%2A%2812%2F-1+-+1%2Ay%2F-1%29+%2B+6%5Cy+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=30. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12%2F-1+-+1%2Ay%2F-1 ALIGN=MIDDLE  ALT=\"x+=+12%2F-1+-+1%2Ay%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=18.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=18%2C+y=30+%29 ALIGN=MIDDLE  ALT=\"system%28+x=18%2C+y=30+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Step 6.  The numbers are 18 and 30.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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