document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138269>Question 1138269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two shelves contain 55 books. If half of the books from the second shelf were relocated to the first shelf, then the first shelf would contain 4 times as many books as the second one. How many books are there on each shelf?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756095 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=756095\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the number of books on the first shelf.<BR>\n" );
document.write( "let y equal the number of books on the second shelf.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if half of the books from the second shelf were relocated to the first shelf, then the first shelf would contain 4 times as many books as the second shelf.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for this is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 1/2 * y = 4 * (1/2 * y).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get x + 1/2 * y = 2 * y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by 2 to get 2x + y = 4y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract y from both sides of the equation to get 2x = 3y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y in the first equation of x + y = 55 to get y = 55 - x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with 55 - x in the equation of 2x = 3y to get 2x = 3 * (55 - x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get 2x = 165 - 3x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add 3x to both sides of this equation to get 5x = 165.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 33.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y = 55, then y = 22.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have x = 33 and y = 22.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y = 33 + 22 = 55\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take away half of y and add it to x to get x = 44, leaving y to be equal to 11.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "44 is equal to 4 * 11, confirming the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there were originally 33 books on the first shelf and 22 books on the second shelf.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after the relocation, there are 44 books on the first shelf and 11 books on the second shelf.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );