document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758461>Question 758461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the difference between two numbers is eight. If the smaller number exceeds half of the larger number by fourteen, what are 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 #461482 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=461482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a represent the larger number<BR>\n" );
document.write( "let b represent the smaller number\r<BR>\n" );
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document.write( "formulas become:\r<BR>\n" );
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document.write( "a - b = 8 (difference between the numbers is 8).<BR>\n" );
document.write( "b > (a/2) + 14 (smaller numbrer exceeds 1/2 * bigger number by 14)<BR>\n" );
document.write( "solve for b in the first equationj to get b = a - 8<BR>\n" );
document.write( "substitute for b in the second equation to get:<BR>\n" );
document.write( "a - 8 > (a/2) + 14<BR>\n" );
document.write( "multiply both sides of this equationm by 2 to get:<BR>\n" );
document.write( "2a - 16 > a + 28<BR>\n" );
document.write( "subtract a from both sides of this equation and add 16 to both sides of this equation to get:<BR>\n" );
document.write( "2a - a > 28 + 16<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "a > 44<BR>\n" );
document.write( "when a > 44, both equations will be satisfied.<BR>\n" );
document.write( "as an example, let a = 50<BR>\n" );
document.write( "when a = 50, 50 - b = 8 which makes b = 42<BR>\n" );
document.write( "you have a  50 and b = 42<BR>\n" );
document.write( "first equation is satisfied because 50 - 42 = 8<BR>\n" );
document.write( "second equation becomes:<BR>\n" );
document.write( "42 > (50/2) + 14 which becomes:<BR>\n" );
document.write( "42 > 25 + 14 which becomes:<BR>\n" );
document.write( "42 > 39 which is true so the second equation is satisfied as well.<BR>\n" );
document.write( "since both equations are satisfied, your answer is a > 44.<BR>\n" );
document.write( "you can also confirm by making a = 44 and a < 44 and seeing that the equation is not satisfied.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "let a = 44<BR>\n" );
document.write( "this makes b = 36<BR>\n" );
document.write( "first equation is satisfied because 44 - 36 = 8<BR>\n" );
document.write( "second equation becomes:<BR>\n" );
document.write( "36 > (44/2) + 14 which becomes:<BR>\n" );
document.write( "36 > 22 + 14 which becomes:<BR>\n" );
document.write( "36 > 36 which is NOT true because 36 = 36.<BR>\n" );
document.write( "when a < 44, you will get similar results.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "let a = 40<BR>\n" );
document.write( "this makes b = 32<BR>\n" );
document.write( "first equation is satisfied because 40 - 32 = 8<BR>\n" );
document.write( "second equation becomes:<BR>\n" );
document.write( "32 > (40/2) + 14 which becomes:<BR>\n" );
document.write( "32 > 20 + 14 which becomes:<BR>\n" );
document.write( "32 > 34 which is not true because 32 < 34.<BR>\n" );
document.write( "the solution of a > 44 is good because:<BR>\n" );
document.write( "when a > 44 both equations are satisfied.<BR>\n" );
document.write( "when a <= 44 both equations are not satisfied.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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