document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358073>Question 358073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twice the small number is 5 more than 2/3 the larger number. Three times the larger number is 4 less than 15 times the smaller number.  Find the value of 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 #255658 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=255658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the large number<BR>\n" );
document.write( "Let y = the small number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Twice the small number is 5 more than 2/3 the larger number.<BR>\n" );
document.write( "2y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 5<BR>\n" );
document.write( "Get rid of that annoying fraction, multiply by 3, results:<BR>\n" );
document.write( "6y = 2x + 15<BR>\n" );
document.write( "-2x + 6y = 15<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Three times the larger number is 4 less than 15 times the smaller number.<BR>\n" );
document.write( "3x = 15y - 4<BR>\n" );
document.write( "3x - 15y = -4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination here, multiply the 1st equation by 3, and the 2nd equation by 2<BR>\n" );
document.write( "-6x + 18y = 45<BR>\n" );
document.write( "+6x - 20y = -8<BR>\n" );
document.write( "-------------------adding eliminates x, find y<BR>\n" );
document.write( "-12y = 37<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F12 ALIGN=MIDDLE  ALT=\"-37%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the 1st equation to find x<BR>\n" );
document.write( "-2x + 6(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F12 ALIGN=MIDDLE  ALT=\"-37%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 15<BR>\n" );
document.write( "-2x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F2 ALIGN=MIDDLE  ALT=\"-37%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = 15<BR>\n" );
document.write( "Multiply by 2<BR>\n" );
document.write( "-4x - 37 = 30<BR>\n" );
document.write( "-4x = 30 + 37<BR>\n" );
document.write( "-4x = 67<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-67%2F4 ALIGN=MIDDLE  ALT=\"-67%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "A couple nasty fractions, see if they work in the 2nd equation<BR>\n" );
document.write( "3x - 15y = -4<BR>\n" );
document.write( "Substitute<BR>\n" );
document.write( "3(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-67%2F4 ALIGN=MIDDLE  ALT=\"-67%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) - 15(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-37%2F12 ALIGN=MIDDLE  ALT=\"-37%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-201%2F4 ALIGN=MIDDLE  ALT=\"-201%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=555%2F12 ALIGN=MIDDLE  ALT=\"555%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -4<BR>\n" );
document.write( "multiply by 12 to get rid of those annoying fractions<BR>\n" );
document.write( "3(201) + 555 = -48<BR>\n" );
document.write( "-603 + 555 = -48; it does work, amazing isn't it!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );