document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210324>Question 1210324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of the ages of Adu and Tanko is 9 less than Akorfa's age. If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851900 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=851900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The editorial comment from tutor @ikleyn that it is \"obvious\" that the objective of the problem is to solve it using a single variable is a bit arrogant; solving the problem using three variables is a perfectly good exercise.<br><BR>\n" );
document.write( "And while it is possible to solve the problem using an online problem solver, as tutor Edwin shows, probably the objective of the problem is to help the student learn to solve it algebraically.<br><BR>\n" );
document.write( "So....<br><BR>\n" );
document.write( "a = Adu's age<BR>\n" );
document.write( "t = Tanko's age<BR>\n" );
document.write( "k = Akorfa's age<br><BR>\n" );
document.write( "The given information, translated directly to algebraic equations, is the following:<br><BR>\n" );
document.write( "(1) at = k-9<BR>\n" );
document.write( "(2) t = a+4<BR>\n" );
document.write( "(3) k = 6t<br><BR>\n" );
document.write( "Substitute (2) into (3):<BR>\n" );
document.write( "(4) k = 6(a+4)<br><BR>\n" );
document.write( "Substitute (2) and (4) into (1):<BR>\n" );
document.write( "a(a+4) = 6(a+4)-9<BR>\n" );
document.write( "a^2+4a = 6a+24-9 = 6a+15<BR>\n" );
document.write( "a^2-2a-15 = 0<BR>\n" );
document.write( "(a-5)(a+3) = 0<br><BR>\n" );
document.write( "Adu's age could be either 5 or -3.  The negative age clearly makes no sense, so Adu's age is 5.<br><BR>\n" );
document.write( "a = 5<BR>\n" );
document.write( "from (2), t = 5+4 = 9<BR>\n" );
document.write( "from (3), k = 6(9) = 54<br><BR>\n" );
document.write( "ANSWER: Akorfa's age is 54<br><BR>\n" );
document.write( "(and Adu is 5 and Tanko is 9....)<br><BR>\n" );
document.write( "--------------------------------------------------------<br><BR>\n" );
document.write( "added after seeing the response from tutor @ikleyn to my response....<br><BR>\n" );
document.write( "Dear tutor @ikleyn<br><BR>\n" );
document.write( "By saying in your response that that it is \"obvious\" that THE way to solve the problem is using a single variable, you ARE being arrogant.<br><BR>\n" );
document.write( "Of course you wouldn't recognize it as arrogance, because arrogant is the way you are.<br><BR>\n" );
document.write( "Recall the recent pair of twin problems where you posted identical wrong solutions, then when other tutors posted correct solutions you insisted your solution was correct, and even posted the problem to google which came back with an answer different than yours (and the same as ours) and you concluded that google got the wrong answer; then when you took the time to look at your responses you finally saw your error.  The time you spent trying to show that your solutions were correct, and the time that you spent writing your vitriolic attacks on the correct responses of other tutors, was far more time than would have been required for you to look at your original responses and see your errors.<br><BR>\n" );
document.write( "That is a display of arrogance if I ever saw one.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );