document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251564>Question 251564</A>: <I><SPAN STYLE=\"word-break: break-all;\">  hi im a 13 year old boy in 8th grade in algerbra 1 honors class. im really stumped on these questions and need some help please. Please help me and thank you very much. merry early christmas!!<BR>\n" );
document.write( "(1)The sum of the reciprocals of two consecutive odd integers is 8/15. find the number. <BR>\n" );
document.write( "(2)The sum of the reciprocals of two consecutive even integers is 11/60. find the integers.<BR>\n" );
document.write( "(3) the sum of two numbers is 10 and the sum of there reciprocals is 5/12. 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 #183266 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=183266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1)The sum of the reciprocals of two consecutive odd integers is 8/15. find the number.<BR>\n" );
document.write( "Odd numbers are always one more than or one less than an even number.<BR>\n" );
document.write( "Symbols for an odd number are 2x-1 or 2x+1<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Your problem:<BR>\n" );
document.write( "1st odd: 2x-1<BR>\n" );
document.write( "Next consecutive odd: 2x+1<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "1/(2x-1) + 1/(2x+1) = 8/15<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Multiply thru by 15(2x-1)(2x+1):<BR>\n" );
document.write( "15(2x+1) + 15(2x-1) = 8(2x+1)(2x-1)<BR>\n" );
document.write( "30x+15 + 30x-15 = 8(4x^2-1)<BR>\n" );
document.write( "60x = 32x^2-8<BR>\n" );
document.write( "32x^2-60x-8 = 0<BR>\n" );
document.write( "8x^2-15x-2 = 0<BR>\n" );
document.write( "8x^2-16x+x-2 = 0<BR>\n" );
document.write( "8x(x-2)+(x-2) = 0<BR>\n" );
document.write( "(x-2)(8x+1) = 0<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "1st odd: 2x-1 = 3<BR>\n" );
document.write( "2nd odd: 2x+1 = 5<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "Checking<BR>\n" );
document.write( "1/3 + 1/5 = 8/15<BR>\n" );
document.write( "Multiply thru by 15:<BR>\n" );
document.write( "5 + 3 = 8<BR>\n" );
document.write( "8 = 8<BR>\n" );
document.write( "=================\r<BR>\n" );
document.write( "\n" );
document.write( "(2)The sum of the reciprocals of two consecutive even integers is 11/60. find the integers.<BR>\n" );
document.write( "Follow the same procedure as in #1 but use the followin symbols<BR>\n" );
document.write( "for consecutive even numbers.<BR>\n" );
document.write( "1st: 2x<BR>\n" );
document.write( "2nd: 2x+2<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "(3) the sum of two numbers is 10 and the sum of their reciprocals is 5/12. <BR>\n" );
document.write( "Find the numbers.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "x + y = 10<BR>\n" );
document.write( "1/x + 1/y = 5/12<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Rearrange the equations:<BR>\n" );
document.write( "x = 10-y<BR>\n" );
document.write( "12y + 12x = 5xy<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Substitute for \"x\" and solve for \"y\":<BR>\n" );
document.write( "12y + 12(10-y) = 5(10-y)y<BR>\n" );
document.write( "12y + 120 - 12y = 50y - 5y^2<BR>\n" );
document.write( "5y^2 -50y+120 = 0<BR>\n" );
document.write( "y^2 - 10y + 24 = 0<BR>\n" );
document.write( "(y-6)(y-4) = 0<BR>\n" );
document.write( "y = 6 or y = 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Substitute into x 10-y<BR>\n" );
document.write( "If y = 6, x= 4<BR>\n" );
document.write( "If y = 4, y = 6<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Checking:<BR>\n" );
document.write( "x+y = 10<BR>\n" );
document.write( "4+6 = 10<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "1/4 + 1/6 = 5/12<BR>\n" );
document.write( "Multiply thru by 12 to get:<BR>\n" );
document.write( "3+2 = 5<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );