document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340301>Question 340301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 12 degrees less than one third of the larger is 4 degrees more than the smaller.Find the measure of each angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243817 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=243817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the smaller.<BR>\n" );
document.write( "Let y be the larger.<BR>\n" );
document.write( "1/3 * y - 12 = x + 4<BR>\n" );
document.write( "Add 12 to both sides of the equation to get:<BR>\n" );
document.write( "1/3 * y = x + 16<BR>\n" );
document.write( "Multiply both sides of the equation by 3 to get:<BR>\n" );
document.write( "y = 3x + 48<BR>\n" );
document.write( "For every value of x, y can be found using that formula, it seems.<BR>\n" );
document.write( "If x = 1, then y = 51<BR>\n" );
document.write( "If x = 2, then y = 54<BR>\n" );
document.write( "If x = 3, then  y = 57<BR>\n" );
document.write( "To test this out, substitute in the original equations.<BR>\n" );
document.write( "The original equation states:<BR>\n" );
document.write( "12 degrees less than one third of the larger is 4 degrees more than the smaller.<BR>\n" );
document.write( "If the larger is 57, then 1/3 of that is 19 and 12 less than that is 7.  Since 7 is 4 more than 3, the equation holds.<BR>\n" );
document.write( "If the larger is 51, then 1/3 of that is 17 and 12 less than that is 5.  Since 5 is 4 more than 1, the equation holds.<BR>\n" );
document.write( "Your solution does not lend itself to one unique angle.<BR>\n" );
document.write( "The value of each angle is dependent on the value of the other.<BR>\n" );
document.write( "Assume the larger angle is 85 degrees.<BR>\n" );
document.write( "1/3 of 85 = 28 and 1/3 degrees.<BR>\n" );
document.write( "12 less than is 16 and 1/3 degrees.<BR>\n" );
document.write( "4 more than that is 20 and 1/3 degrees.<BR>\n" );
document.write( "If the larger angle is 85 degrees, then the smaller angle has to be 20 and 1/3 degrees.<BR>\n" );
document.write( "Working backward, 20 and 1/3 degrees minus 4 = 16 and 1/3 degree.<BR>\n" );
document.write( "12 more than that is 28 and 1/3 degrees.<BR>\n" );
document.write( "3 times that is 84 and 3/3 degrees which is equal to 85 degrees.<BR>\n" );
document.write( "The angles can be anything as long as they keep the fixed relationship between them represented by the formula.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );