document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165142>Question 165142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find two numbers such that five times the larger plud three times the smaller is 47 and four times the larger minus twice the smaller is 20. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121721 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let S = smaller number<BR>\n" );
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document.write( "L = larger number<BR>\n" );
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document.write( "Since we have two unknowns, we'll need two equations.<BR>\n" );
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document.write( "Equation 1: \"five times the larger plus three times the smaller is 47\"<BR>\n" );
document.write( "5L + 3S = 47<BR>\n" );
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document.write( "Equation 2: \"four times the larger minus twice the smaller is 20\"<BR>\n" );
document.write( "4L - 2S = 20<BR>\n" );
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document.write( "Using the \"substitution method\", solve equation 2 for S:<BR>\n" );
document.write( "4L - 2S = 20<BR>\n" );
document.write( "4L = 2S + 20<BR>\n" );
document.write( "4L-20 = 2S<BR>\n" );
document.write( "2L-10 = S<BR>\n" );
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document.write( "Substitute the above into equation 1 and solve for L:<BR>\n" );
document.write( "5L + 3S = 47<BR>\n" );
document.write( "5L + 3(2L-10) = 47<BR>\n" );
document.write( "5L + 6L-30 = 47<BR>\n" );
document.write( "11L - 30 = 47<BR>\n" );
document.write( "11L = 77<BR>\n" );
document.write( "L = 7<BR>\n" );
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document.write( "Finally, plug the above back into equation 2 and solve for S:<BR>\n" );
document.write( "4L - 2S = 2<BR>\n" );
document.write( "4(7) - 2S = 2<BR>\n" );
document.write( "28 - S = 1<BR>\n" );
document.write( "28 = S + 1<BR>\n" );
document.write( "27 = S<BR>\n" );
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document.write( "Solution: The two numbers are 7 and 27<BR>\n" );
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