document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184410>Question 1184410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Gab’s age on his birthday in 1989 is equal to the sum of the digits of the year 19xy in which he was born. If x and y satisfies the equation x  -  y  -  6 = 0, find the age of Gab in 1990. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814979 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=814979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "x-y-6=0  ==>  x = y+6<br><BR>\n" );
document.write( "Since x and y are both single-digit integers, there are only a few possibilities.  Solving the problem by trial and error is probably easier than solving it using formal algebra.<br><BR>\n" );
document.write( "y=0, x=6  ==>  he was born in 1960; his age in 1989 was 29; 1+9+6+0 is not equal to 29.  Doesn't work.<br><BR>\n" );
document.write( "y=1, x=7  ==>  he was born in 1971; his age in 1989 was 18; 1+9+7+1 = 18.  It works!<br><BR>\n" );
document.write( "So Gabe was born in  1971.<br><BR>\n" );
document.write( "ANSWER: Gabe's age in 1990 was 1990-1971 = 19<br><BR>\n" );
document.write( "It turns out that a solution using formal algebra is relatively easy....<br><BR>\n" );
document.write( "His age in 1989 is the difference between 89 and \"xy\", which algebraically is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89-%2810x%2By%29=89-10x-y ALIGN=MIDDLE  ALT=\"89-%2810x%2By%29=89-10x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "His age in 1989 is equal to the sum of the digits of the year in which he was born:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=89-10x-y=1%2B9%2Bx%2By ALIGN=MIDDLE  ALT=\"89-10x-y=1%2B9%2Bx%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79=11x%2B2y ALIGN=MIDDLE  ALT=\"79=11x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Given the restriction that x and y are both single digit positive integers, the only solution to that equation is x=7 and y=1.<br><BR>\n" );
document.write( "Of course you could finish that last step still using formal algebra, knowing that x=y+6:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79=11x%2B2y ALIGN=MIDDLE  ALT=\"79=11x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79=11%28y%2B6%29%2B2y ALIGN=MIDDLE  ALT=\"79=11%28y%2B6%29%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=79=11y%2B66%2B2y=13y%2B66 ALIGN=MIDDLE  ALT=\"79=11y%2B66%2B2y=13y%2B66\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13=13y ALIGN=MIDDLE  ALT=\"13=13y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B6=7 ALIGN=MIDDLE  ALT=\"x=y%2B6=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So again (of course!) we find he was born in 1971, which means his age in 1990 was 19.<br><BR>\n" );
document.write( " </SPAN>\n" );
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