document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=133416>Question 133416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago, Carl's age was 3 years less than twice the sum of the girls' ages then. How old is Carl now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97590 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=97590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alice is 4 years younger than Betty and Carl is 3 times as old as Alice. Five years ago, Carl's age was 3 years less than twice the sum of the girls' ages then. How old is Carl now?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Alice now: a<BR>\n" );
document.write( "Betty now: b<BR>\n" );
document.write( "Carl now: c\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b-4 ALIGN=MIDDLE  ALT=\"a=b-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Alice is 4 years younger than Betty<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3a ALIGN=MIDDLE  ALT=\"c=3a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Carl five years ago: c - 5<BR>\n" );
document.write( "Alice five years ago: a - 5<BR>\n" );
document.write( "Betty five years ago: b - 5\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of the girls' ages five years ago: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-5%29%2B%28b-5%29 ALIGN=MIDDLE  ALT=\"%28a-5%29%2B%28b-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Twice the sum... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%28a-5%29%2B%28b-5%29%29=2a%2B2b-20 ALIGN=MIDDLE  ALT=\"2%28%28a-5%29%2B%28b-5%29%29=2a%2B2b-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Carl five years ago was 3 years less than the above expression, so:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c-5=2a%2B2b-20-3 ALIGN=MIDDLE  ALT=\"c-5=2a%2B2b-20-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2a%2B2b-18 ALIGN=MIDDLE  ALT=\"c=2a%2B2b-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b-4 ALIGN=MIDDLE  ALT=\"a=b-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+a%2B4 ALIGN=MIDDLE  ALT=\"b+=+a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now substitute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=2a%2B2%28a%2B4%29-18 ALIGN=MIDDLE  ALT=\"3a=2a%2B2%28a%2B4%29-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=2a%2B2a%2B8-10 ALIGN=MIDDLE  ALT=\"3a=2a%2B2a%2B8-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=4a-10 ALIGN=MIDDLE  ALT=\"3a=4a-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a=-10 ALIGN=MIDDLE  ALT=\"-a=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=10 ALIGN=MIDDLE  ALT=\"a=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So Alice is 10 now, which means that Betty is 10 + 4 = 13, and Carl is 3 * 10 = 30.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Check the answer:<BR>\n" );
document.write( "5 years ago, Carl would have been 25, Alice, 5, and Betty, 9.  the sum of their ages then would have been 14, twice 14 is 28, 3 years less than that is 25.  Answer checks. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );