document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106284>Question 106284</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395676088/algebrahomeworkh>Algabra Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The difference of two integers is 9.  Five times the smaller is 7 more than three times the larger.  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 #77335 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Let x=the larger integer<BR>\n" );
document.write( "And let y=the smaller integer\r<BR>\n" );
document.write( "\n" );
document.write( "Now we are told that x-y=9--------------------------eq1\r<BR>\n" );
document.write( "\n" );
document.write( "We are also told that 5y=3x+7-----------------------eq2\r<BR>\n" );
document.write( "\n" );
document.write( "From eq1, substitute x=y+9 into eq2 and we get:\r<BR>\n" );
document.write( "\n" );
document.write( "5y=3(y+9)+7  get rid of parens\r<BR>\n" );
document.write( "\n" );
document.write( "5y=3y+27+7  subtract 3y from both sides<BR>\n" );
document.write( "5y-3y=3y-3y+27+7  collect like terms<BR>\n" );
document.write( "2y=34  divide both sides by 2\r<BR>\n" );
document.write( "\n" );
document.write( "y=17------------------the smaller integer<BR>\n" );
document.write( "From eq1, x=9+y=9+17=26 --------the larger integer\r<BR>\n" );
document.write( "\n" );
document.write( "CK\r<BR>\n" );
document.write( "\n" );
document.write( "x-y=9<BR>\n" );
document.write( "26-17=9<BR>\n" );
document.write( "9=9<BR>\n" );
document.write( "also<BR>\n" );
document.write( "5y=3x+7<BR>\n" );
document.write( "5*17=3*26+7\r<BR>\n" );
document.write( "\n" );
document.write( "85=78+7<BR>\n" );
document.write( "85=85\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another way to solve this problem:\r<BR>\n" );
document.write( "\n" );
document.write( "Let x=the larger integer<BR>\n" );
document.write( "Then x-9= the smaller integer \r<BR>\n" );
document.write( "\n" );
document.write( "Now we are told that:\r<BR>\n" );
document.write( "\n" );
document.write( "5(x-9)=3x+7  get rid of parens\r<BR>\n" );
document.write( "\n" );
document.write( "5x-45=3x+7  subtract 3x from and add 45 to both sides\r<BR>\n" );
document.write( "\n" );
document.write( "5x-3x-45+45=3x-3x+45+7  collect like terms\r<BR>\n" );
document.write( "\n" );
document.write( "2x=52  divide both sides by 2\r<BR>\n" );
document.write( "\n" );
document.write( "x=26----------------the larger integer\r<BR>\n" );
document.write( "\n" );
document.write( "x-9=26-9=17---------------the smaller integer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps----ptaylor\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );