document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600129>Question 600129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379183 by </B><A HREF=/tutors/aboutme.mpl?userid=godsgirls><B>godsgirls(5)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=godsgirls><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=379183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 50. Two times the smaller number exceeds the larger number by 31. Find the numbers.\r<BR>\n" );
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document.write( "First we need to write out equations. Let x equal the first number and y equal the second. The sum of two numbers is 50: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+50 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Two times the smaller number (we'll make that x) exceeds the larger number (y) by 31. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+y+%2B31 ALIGN=MIDDLE  ALT=\"2x+=+y+%2B31\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here I'm going to teach you a trick that will become handy once you get into high school math. <BR>\n" );
document.write( "It's called combining equations. <BR>\n" );
document.write( "First we need to multiply the first equation by 2. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax+%2B+2%2Ay+=+2%2A50 ALIGN=MIDDLE  ALT=\"2%2Ax+%2B+2%2Ay+=+2%2A50\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y+=+100 ALIGN=MIDDLE  ALT=\"2x+%2B+2y+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "of course, we know from our second equation that 2x = y + 31. So we substitute this into our first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+31+%2B+2y+=+100 ALIGN=MIDDLE  ALT=\"y+%2B+31+%2B+2y+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Combine like terms to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+31+=+100 ALIGN=MIDDLE  ALT=\"3y+%2B+31+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract 31 from each side: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+31+-+31+=+100+-+31 ALIGN=MIDDLE  ALT=\"3y+%2B+31+-+31+=+100+-+31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+=+61 ALIGN=MIDDLE  ALT=\"3y+=+61\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by three to isolate y. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2F3+=+61%2F3 ALIGN=MIDDLE  ALT=\"3y%2F3+=+61%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "this becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+23 ALIGN=MIDDLE  ALT=\"y+=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we have y, we can use our first equation to find x. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+50 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute 23 for y: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+23+=+50 ALIGN=MIDDLE  ALT=\"x+%2B+23+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "subtract 23 from each side. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+23+-+23+=+50+-+23 ALIGN=MIDDLE  ALT=\"x+%2B+23+-+23+=+50+-+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+27 ALIGN=MIDDLE  ALT=\"x+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So your two numbers are 27 and 23. I hope this helps you!\r<BR>\n" );
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