document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212175>Question 212175</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073206042/algebrahomeworkh>Elementary And Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Ancient history.  This problem is from the second century.  Four numbers have a sum of 9900.  The second exceeds the first by one-seventh of the first.  The third exceeds the sum of the first two by 300.  The fourth exceeds the sum of the first three by 300.  Find the four numbers.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160274 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=160274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is from the second century. Four numbers have a sum of 9900.<BR>\n" );
document.write( " The second exceeds the first by one-seventh of the first. <BR>\n" );
document.write( "The third exceeds the sum of the first two by 300. <BR>\n" );
document.write( "The fourth exceeds the sum of the first three by 300. Find the four numbers. <BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "Four numbers have a sum of 9900.<BR>\n" );
document.write( "w + x + y + z = 9900<BR>\n" );
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document.write( "The second exceeds the first by one-seventh of the first.<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F7 ALIGN=MIDDLE  ALT=\"8%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >w<BR>\n" );
document.write( "Multiply both sides by 7<BR>\n" );
document.write( "7x = 8w<BR>\n" );
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document.write( "The third exceeds the sum of the first two by 300.<BR>\n" );
document.write( "y = w + x + 300<BR>\n" );
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document.write( "The fourth exceeds the sum of the first three by 300.<BR>\n" );
document.write( "z = w + x + y + 300<BR>\n" );
document.write( "Rearrange and subtract from the 1st equation:<BR>\n" );
document.write( "w + x + y + z = 9900<BR>\n" );
document.write( "w + x + y - z = -300<BR>\n" );
document.write( "----------------------eliminates w, x, y<BR>\n" );
document.write( "2z = 10200<BR>\n" );
document.write( "z = 5100<BR>\n" );
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document.write( "Using the 1st equation replace z with 5100 <BR>\n" );
document.write( "w + x + y + 5100 = 9900<BR>\n" );
document.write( "w + x + y = 9900 - 5100<BR>\n" );
document.write( "w + x + y = 4800<BR>\n" );
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document.write( "Rearrange the 3rd equation to: w + x - y = -300 subtract from the above eq;<BR>\n" );
document.write( "w + x + y = 4800<BR>\n" );
document.write( "w + x - y = -300<BR>\n" );
document.write( "------------------eliminate w and x<BR>\n" );
document.write( "2y = 5100<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5100%2F2 ALIGN=MIDDLE  ALT=\"5100%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 2550<BR>\n" );
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document.write( "Using the 1st equation replace y and z<BR>\n" );
document.write( "w + x + 2550 + 51000 = 9900 <BR>\n" );
document.write( "w + x = 9900 - 2550 - 5100<BR>\n" );
document.write( "w + x = 2250<BR>\n" );
document.write( "w = (2250 - x); use for substitution<BR>\n" );
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document.write( "Using 7x = 8w, replace w, find x<BR>\n" );
document.write( "7x = 8(2250-x)<BR>\n" );
document.write( "7x = 18000 - 8x<BR>\n" );
document.write( "7x + 8x = 18000<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18000%2F15 ALIGN=MIDDLE  ALT=\"18000%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1200<BR>\n" );
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document.write( "w = 2250 - x; replace x<BR>\n" );
document.write( "w = 2250 - 1200<BR>\n" );
document.write( "w = 1050<BR>\n" );
document.write( ";<BR>\n" );
document.write( "The 4 numbers<BR>\n" );
document.write( "w = 1050<BR>\n" );
document.write( "x = 1200<BR>\n" );
document.write( "y = 2550<BR>\n" );
document.write( "z = 5100<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "tot:9900\r<BR>\n" );
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