document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167656>Question 167656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain triangle the measure of one angle is double the measure of a second angle, but is five degress less than the measure of the third angle. If the sum of the measures of the 3 interior angles is always 180 form an algebraic equation to express the problem?\r<BR>\n" );
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document.write( "I came up with a+2a-5=180, but this just doesn't seem right to me, could you please help? Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123558 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the angles of the triangle be a, b, and c.<BR>\n" );
document.write( "let a = 2*b<BR>\n" );
document.write( "let a = c-5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if a = 2*b, then b = a/2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if a = c-5, then c = a+5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the sum of the interior angles of a triangle = 180 degrees, then<BR>\n" );
document.write( "a + b + c = 180<BR>\n" );
document.write( "substituting a/2 for b, and a+5 for c, we get:<BR>\n" );
document.write( "a + a/2 + a + 5 = 180<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "combining like terms, we get:<BR>\n" );
document.write( "2*a + a/2 + 5 = 180<BR>\n" );
document.write( "subtracting 5 from both side of the equation we get:<BR>\n" );
document.write( "2*a + a/2 = 175<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since 2*a is the same as 4*a/2, we can substitute to get:<BR>\n" );
document.write( "4*a/2 + a/2 = 175<BR>\n" );
document.write( "since the denominators on the left hand side of the equation are the same, this equation becomes:<BR>\n" );
document.write( "(4*a + a)/2 = 175<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "(5*a)/2 = 175<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiplying both sides of the equation by 2 gets:<BR>\n" );
document.write( "5*a = 350<BR>\n" );
document.write( "dividing both sides of the equation by 5 gets:<BR>\n" );
document.write( "a = 70<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a = 70<BR>\n" );
document.write( "b = a/2 = 35<BR>\n" );
document.write( "c = a+5 = 75<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "70 + 35 + 75 = 180<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "algebraic expression to solve the problem was derived above.<BR>\n" );
document.write( "it started off as<BR>\n" );
document.write( "a+b+c = 180<BR>\n" );
document.write( "we solved for b in terms of a.<BR>\n" );
document.write( "we solved for c in terms of a.<BR>\n" );
document.write( "equation became:<BR>\n" );
document.write( "a + (a/2) + (a+5) = 180<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the rest was simplification to come up with a = 70.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
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