document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105576>Question 1105576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "ben and tom had a total of 144 sweets.ben gave tom 1/5 of what he had. Tom the gave ben 1/4 of what he had to ben. If both had an equal number of sweets in the end, how many did each of them have at first. \r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720440 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There was an error in the algebra in the solution provided by the other tutor; the given answer does not satisfy the conditions in the problem.<br><BR>\n" );
document.write( "Let b and t represent the numbers Ben and Tom start out with, respectively:<BR>\n" );
document.write( "Start:<BR>\n" );
document.write( "Ben = b;<BR>\n" );
document.write( "Tom = t.<br><BR>\n" );
document.write( "Ben gives 1/5 of the number he has to Tom; after that:<BR>\n" );
document.write( "Ben = (4/5)b;<BR>\n" );
document.write( "Tom = t+(1/5)b.<br><BR>\n" );
document.write( "Tom now gives 1/4 of what he has  -- which is (1/4)t+(1/20)b -- to Ben; after that:<BR>\n" );
document.write( "Ben = (4/5)b+(1/4)t+(1/20)b = (17/20)b+(1/4)t;<BR>\n" );
document.write( "Tom = (3/4)t+(3/20)b.<br><BR>\n" );
document.write( "At this point the two of them have the same number of sweets, 72.<br><BR>\n" );
document.write( "Ben: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2817%2F20%29b%2B%281%2F4%29t+=+72 ALIGN=MIDDLE  ALT=\"%2817%2F20%29b%2B%281%2F4%29t+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17b%2B5t=1440 ALIGN=MIDDLE  ALT=\"17b%2B5t=1440\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Tom: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29t%2B%283%2F20%29b+=+72 ALIGN=MIDDLE  ALT=\"%283%2F4%29t%2B%283%2F20%29b+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15t%2B3b=1440 ALIGN=MIDDLE  ALT=\"15t%2B3b=1440\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve (1) and (2) by elimination:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15t%2B51b+=+4320 ALIGN=MIDDLE  ALT=\"15t%2B51b+=+4320\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15t%2B3b+=+1440 ALIGN=MIDDLE  ALT=\"15t%2B3b+=+1440\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48b+=+2880 ALIGN=MIDDLE  ALT=\"48b+=+2880\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+60 ALIGN=MIDDLE  ALT=\"b+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Ben started with 60 sweets; Tom with 84.<br><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "Start: Ben 60, Tom 84<BR>\n" );
document.write( "After Ben gives 1/5 of his to Tom: Ben 60-12 = 48; Tom 84+12 = 96<BR>\n" );
document.write( "After Tom gives 1/4 of his to Ben: Ben 48+24 = 72; Tom 96-24 = 72<BR>\n" );
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