document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419510>Question 419510</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ruth is 22 years older than her son. 7 years ago ruth was 3 times her sons age... how old are they now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293357 by </B><A HREF=/tutors/aboutme.mpl?userid=duckness73><B>duckness73(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=duckness73><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=duckness73><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r = Ruth's age today<BR>\n" );
document.write( "Let s = Son's age today\r<BR>\n" );
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document.write( "Since Ruth is 22 years older than her son, r = s + 22.<BR>\n" );
document.write( "Seven years ago, when Ruth was r - 7 and her son was s - 7, Ruth was 3 time older than her son which means that r - 7 = 3(s - 7)  So we have simultaneous equations:\r<BR>\n" );
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document.write( "r = s + 22<BR>\n" );
document.write( "r - 7 = 3(s - 7)\r<BR>\n" );
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document.write( "Substituting the value of r from the first equation into the second equations, we have:\r<BR>\n" );
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document.write( "(s + 22) - 7 = 3(s - 7)<BR>\n" );
document.write( "s + 15 = 3s - 21<BR>\n" );
document.write( "15 = 2s - 21<BR>\n" );
document.write( "36 = 2s<BR>\n" );
document.write( "18 = s  the son's age<BR>\n" );
document.write( "r = s + 22 = 18 + 22 = 40 which is Ruth's age.\r<BR>\n" );
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document.write( "Today, Ruth is 40 and her son is 18. </SPAN>\n" );
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