document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202434>Question 1202434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tim and Tala are brother and sister. Their ages total 36. The difference between twice Tala's age and Tim's age is 12. Find their ages. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837274 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</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=837274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Note that you have received two earlier responses, one showing a single solution and another showing two solutions.<br><BR>\n" );
document.write( "If we want to be mathematically correct, there is only the one solution.  The second solution is possible only if we don't follow strict mathematical rules.<br><BR>\n" );
document.write( "In everyday English usage, the difference between 5 and 3 is 2, and the difference between 3 and 5 is 2.  The order is not important; the difference is always considered to be positive (or non-negative).<br><BR>\n" );
document.write( "However, in mathematics, the order is important.  The difference between a and b is always a-b; it is never b-a.  So in mathematics the difference between 5 and 3 is 2, but the difference between 3 and 5 is -2.<br><BR>\n" );
document.write( "So in your problem, if x is Tim's age and y is Tala's age, then the difference between twice Tala's age and Tim's age is 2y-x.  That leads to the single mathematically correct solution to the problem:<br><BR>\n" );
document.write( "x + y = 36<BR>\n" );
document.write( "2y - x = 12<BR>\n" );
document.write( "3y = 48<BR>\n" );
document.write( "y = 16<BR>\n" );
document.write( "x = 36-16 = 20<br><BR>\n" );
document.write( "ANSWER: Tim 20, Tala 16<br><BR>\n" );
document.write( "With that solution, the difference between twice Tala's age and Tim's age is 12, as it needs to be: 2(16)-20 = 32-20 = 12.<br><BR>\n" );
document.write( "To get the second, mathematically incorrect, answer, we need to have the difference between twice Tala's age and Tim's age in the wrong order:<br><BR>\n" );
document.write( "x + y = 36<BR>\n" );
document.write( "x - 2y = 12<BR>\n" );
document.write( "3y = 24<BR>\n" );
document.write( "y = 8<BR>\n" );
document.write( "x = 36-8 = 28<br><BR>\n" );
document.write( "mathematically incorrect answer: Tim 28, Tala 8<br><BR>\n" );
document.write( "With this incorrect solution, the difference between twice Tala's age and Tim's age is NOT 12: 2(8)-28 = 16-28 = -12.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );