document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171633>Question 171633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number equals the sum of two other numbers. The largest number diminished by 2 equals three times the smallest. The largest increased by 2 equals twice the result of diminishing the middle number by 2. Find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126818 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Three numbers a,b,c.  a the largest, c the smallest<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement arrange each in the standard form:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"A number equals the sum of two other numbers.\"<BR>\n" );
document.write( "a = b + c<BR>\n" );
document.write( "a - b - c = 0<BR>\n" );
document.write( ";<BR>\n" );
document.write( "\"The largest number diminished by 2 equals three times the smallest.\"<BR>\n" );
document.write( "a - 2 = 3c<BR>\n" );
document.write( "a - 3c = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" The largest increased by 2 equals twice the result of diminishing the middle number by 2.\"<BR>\n" );
document.write( "a + 2 = 2(b-2)<BR>\n" );
document.write( "a + 2 = 2b - 4<BR>\n" );
document.write( "a - 2b = -4 -2<BR>\n" );
document.write( "a - 2b = -6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Arrange all three equations and add<BR>\n" );
document.write( "a - b - c = 0<BR>\n" );
document.write( "a +0b -3c = 2<BR>\n" );
document.write( "a -2b +0c = -6<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "3a - 3b - 4c = -4<BR>\n" );
document.write( ";<BR>\n" );
document.write( "From the 1st statement we know a = (b+c), substitute in the above equation<BR>\n" );
document.write( "3(b+c) - 3b - 4c = -4<BR>\n" );
document.write( "3b + 3c - 3b - 4c = -4<BR>\n" );
document.write( "3b - 3b + 3c - 4c = -4<BR>\n" );
document.write( "-c = -4<BR>\n" );
document.write( "c = + 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a, from the 2nd statement a - 2 = 3c, substitute 4 for c<BR>\n" );
document.write( "a - 2 = 3(4)<BR>\n" );
document.write( "a = 12 + 2<BR>\n" );
document.write( "a = 14<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the 1st statement to find b<BR>\n" );
document.write( "14 = b + 4<BR>\n" );
document.write( "b = 10<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check these solutions in each statement </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );