document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048832>Question 1048832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gary is as old as Harry will be when Gary is twice as old as Harry was when Gary’s age was half the sum of their present ages. \r<BR>\n" );
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document.write( "Harry is as old as Gary was when Harry was half the age he will be 10 years from now. \r<BR>\n" );
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document.write( "What is Harry’s age? <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 #664391 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+ ALIGN=MIDDLE  ALT=\"+g+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Gary's age now<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Harry's age now<BR>\n" );
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document.write( "With these types of problems, I start at<BR>\n" );
document.write( "the end of a statement.<BR>\n" );
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document.write( "\"when Gary’s age was half the sum of their present ages.\"<BR>\n" );
document.write( "Gary's age was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+g+%2B+h+%29%2F2+ ALIGN=MIDDLE  ALT=\"+%28+g+%2B+h+%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"as Harry was when Gary’s age was half the sum of their present ages.\"<BR>\n" );
document.write( "Harry was what was Gary's age then plus the difference in<BR>\n" );
document.write( "their ages ( I'm assuming Harry is the older one )<BR>\n" );
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document.write( "Harry's age was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+g+%2B+h+%29+%2F+2+%2B+%28+h+-+g+%29+ ALIGN=MIDDLE  ALT=\"+%28+g+%2B+h+%29+%2F+2+%2B+%28+h+-+g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"when Gary is twice as old as Harry was when Gary’s <BR>\n" );
document.write( "age was half the sum of their present ages.\"<BR>\n" );
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document.write( "This is when Gary is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"as Harry will be when Gary is twice as old as Harry was <BR>\n" );
document.write( "when Gary’s age was half the sum of their present ages. <BR>\n" );
document.write( "This means I have to add the difference in their ages again<BR>\n" );
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document.write( "Harry will be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I am told that Gary is presently this age, so I can say:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Reading the 2nd statement:<BR>\n" );
document.write( "\"when Harry was half the age he will be 10 years from now.\"<BR>\n" );
document.write( "Harry was:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2A%28+h+%2B+10+%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2A%28+h+%2B+10+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "\"as Gary was when Harry was half <BR>\n" );
document.write( "the age he will be 10 years from now.\"<BR>\n" );
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document.write( "Gary was the younger, so I will subtract the difference in their ages<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2A%28+h+%2B+10+%29+-+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2A%28+h+%2B+10+%29+-+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "This is Harry's age now, so I can say:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+%28+g%2Bh+%29+%2B+2%2A%28+h+-+g+%29+%2B+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+g+=+%28+g%2Bh+%29+%2B+2%2A%28+h+-+g+%29+%2B+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+g+%2B+h+%2B+2h+-+2g+%2B+h+-+g+ ALIGN=MIDDLE  ALT=\"+g+=+g+%2B+h+%2B+2h+-+2g+%2B+h+-+g+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+-2g+%2B+4h+ ALIGN=MIDDLE  ALT=\"+g+=+-2g+%2B+4h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3g+=+4h+ ALIGN=MIDDLE  ALT=\"+3g+=+4h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+%283%2F4%29%2Ag+ ALIGN=MIDDLE  ALT=\"+h+=+%283%2F4%29%2Ag+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( It seems that Harry was actually younger )<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2h+=+h+%2B+10+-2%2A%28+h-g+%29+ ALIGN=MIDDLE  ALT=\"+2h+=+h+%2B+10+-2%2A%28+h-g+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+10+-+2h+%2B+2g+ ALIGN=MIDDLE  ALT=\"+h+=+10+-+2h+%2B+2g+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3h+=+2g+%2B+10+ ALIGN=MIDDLE  ALT=\"+3h+=+2g+%2B+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2g+=+3h+-+10+ ALIGN=MIDDLE  ALT=\"+2g+=+3h+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+%283%2F2%29%2Ah+-+5+ ALIGN=MIDDLE  ALT=\"+g+=+%283%2F2%29%2Ah+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+%283%2F4%29%2A%28%28+3%2F2%29%2Ah+-+5+%29+ ALIGN=MIDDLE  ALT=\"+h+=+%283%2F4%29%2A%28%28+3%2F2%29%2Ah+-+5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4h+=+3%2A%283%2F2%29%2Ah+-+20+ ALIGN=MIDDLE  ALT=\"+4h+=+3%2A%283%2F2%29%2Ah+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8h+=+9h+-+40+ ALIGN=MIDDLE  ALT=\"+8h+=+9h+-+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+40+ ALIGN=MIDDLE  ALT=\"+h+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Harry is 40<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+%283%2F2%29%2Ah+-+5+ ALIGN=MIDDLE  ALT=\"+g+=+%283%2F2%29%2Ah+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+%283%2F2%29%2A40+-+5+ ALIGN=MIDDLE  ALT=\"+g+=+%283%2F2%29%2A40+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+60+-+5+ ALIGN=MIDDLE  ALT=\"+g+=+60+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+g+=+55+ ALIGN=MIDDLE  ALT=\"+g+=+55+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "You can go back to the start and try<BR>\n" );
document.write( "to prove this step by step. I'm too<BR>\n" );
document.write( "tired. Hope I got it right!<BR>\n" );
document.write( "Get a 2nd opinion if you like.\r<BR>\n" );
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document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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