document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029397>Question 1029397</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A man whose end was approaching summoned his sons and said: \"Divide my<BR>\n" );
document.write( "money as I shall prescribe.\" To his eldest son, he said, \"You are to have 1 bezant and a seventh of what is left.\" To his second son he said, \"Take 2 bezants and a seventh of what remains.\" To the third son, \"You are to take 3 bezants and a seventh of what is left.\" Thus he gave each son 1 bezant more than the previous son and a seventh of what remained, and to the last son all that was left. After following their father's instructions with care, the sons found that they had shared their inheritance equally. How many sons were there, and how large was the estate ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644535 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=644535\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man whose end was approaching summoned his sons and said: \"Divide my<BR>\n" );
document.write( "money as I shall prescribe.\" <BR>\n" );
document.write( "To his eldest son, he said, \"You are to have 1 bezant and a seventh of what is left.\"<BR>\n" );
document.write( " To his second son he said, \"Take 2 bezants and a seventh of what remains.\"<BR>\n" );
document.write( " To the third son, \"You are to take 3 bezants and a seventh of what is left.\"<BR>\n" );
document.write( " Thus he gave each son 1 bezant more than the previous son and a seventh of what remained, and to the last son all that was left.<BR>\n" );
document.write( " After following their father's instructions with care, the sons found that they had shared their inheritance equally.<BR>\n" );
document.write( " How many sons were there, and how large was the estate ?<BR>\n" );
document.write( ";<BR>\n" );
document.write( "let a = the original amt of the estate (in Bezants)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1st son's share:<BR>\n" );
document.write( "1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(a-1)<BR>\n" );
document.write( "then remaineth<BR>\n" );
document.write( "a - (1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(a-1)) = a - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F7+%2B+a%2F7+-+1%2F7%29 ALIGN=MIDDLE  ALT=\"%287%2F7+%2B+a%2F7+-+1%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = a - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2F7+%2B+6%2F7%29 ALIGN=MIDDLE  ALT=\"%28a%2F7+%2B+6%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%29%2F7+-+6%2F7 ALIGN=MIDDLE  ALT=\"%286a%29%2F7+-+6%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd son's share;<BR>\n" );
document.write( "2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286a%29%2F7+-+6%2F7+-+2%29 ALIGN=MIDDLE  ALT=\"%28%286a%29%2F7+-+6%2F7+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286a%29%2F7+-+6%2F7+-+14%2F7%29 ALIGN=MIDDLE  ALT=\"%28%286a%29%2F7+-+6%2F7+-+14%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286a%29%2F7+-+20%2F7%29 ALIGN=MIDDLE  ALT=\"%28%286a%29%2F7+-+20%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286a%29%2F49+-+20%2F49%29 ALIGN=MIDDLE  ALT=\"%28%286a%29%2F49+-+20%2F49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=98%2F49+%2B+%286a%29%2F49+-+20%2F49 ALIGN=MIDDLE  ALT=\"98%2F49+%2B+%286a%29%2F49+-+20%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%29%2F49+%2B+78%2F49 ALIGN=MIDDLE  ALT=\"%286a%29%2F49+%2B+78%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" >); 2nd son's share<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1st son's share = 2nd son's share<BR>\n" );
document.write( "1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(a-1) = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286a%29%2F49+%2B+78%2F49 ALIGN=MIDDLE  ALT=\"%286a%29%2F49+%2B+78%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Multiply both sides by 49<BR>\n" );
document.write( "49 + 7(a - 1) = 6a + 78<BR>\n" );
document.write( "49 + 7a - 7 = 6a + 78<BR>\n" );
document.write( "7a + 42 = 6a + 78<BR>\n" );
document.write( "7a - 6a = 78 - 42<BR>\n" );
document.write( "a = 36 Bezants was the amt of the Estate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the number of sons:<BR>\n" );
document.write( "1st son: 1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(36 - 1) = 6 Bezants; <BR>\n" );
document.write( "Now we should be able to say their were 36/6 = 6 sons, but lets continue<BR>\n" );
document.write( "Then 30 remaineth<BR>\n" );
document.write( "2nd son: 2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(30-2) = 6 <BR>\n" );
document.write( "Then 24 remaineth<BR>\n" );
document.write( "3rd son: 3 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(24-3) = 6<BR>\n" );
document.write( "then 18 remaineth<BR>\n" );
document.write( "4th son: 4 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(18-4) = 6 <BR>\n" );
document.write( "then 12 remaineth<BR>\n" );
document.write( "5th son: 5 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >(12-5) = 6<BR>\n" );
document.write( "then 6 remaineth for th 6th son\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );