document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958974>Question 958974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of Hanny's and younger brother Robert's ages is 135. When their ages are divided, the quotient is 1 and the remainder is 6. 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 #586099 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=586099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let h = hanny's age.<BR>\n" );
document.write( "let r = robert's age.<BR>\n" );
document.write( "h*r = 135<BR>\n" );
document.write( "h/r = 1 + remainder of 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could use trial and error and you would get the following:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "135 has to be divisible by 5 because the factors have to be integers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is not really stated, but i think it's implied.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "whether this assumption is valid or not, it does lead to an answer that is corroborated by the more advanced solution to come later.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "looking for the two factors that, when multiplied together, equal 135 yields the following.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "135/5 = 27, so 5 * 27 = 135 but 27/5 doesn't have a quotient of 1, so these factors don't work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "135 / 10 = 13.5, so 13.5 * 10 = 135, and 13.5 / 10 give you a quotient of 1 but not a remainder of 6, these factors don't work..\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "135 / 15 = 9, so 15 * 9 = 135, and 15/9 = 1 with a remainder of 6, so this looks like the one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hanny is 15 and roberto is 9 looks like your solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now for the more advanced way to solve it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have h * r = 135\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you also have h / r = 1 + remainder of 6, which can also be shown as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h/r = 1 + (6/r)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h*r = 135<BR>\n" );
document.write( "h/r = 1 + (6/r)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the second equation of h/r = 1 + (6/r), solve for h to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = (1 + 6/r) * r which simplifies to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = (r + 6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the first equation of h*r = 135, replace h with (r + 6) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(r + 6)*r = 135\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r^2 + 6r = 135\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 135 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r^2 + 6r - 135 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(r + 15) * (r - 9) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for r to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = -15 or r = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r can't be negative, so r must be equal to 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the original equation of h*r = 135 can now be solved for h.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this results in h = 15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution is h = 15 and r = 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both methods get the same solution so it looks good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );