document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205903>Question 1205903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square patchwork quilt is made of many small squares.  The quilt is too small to place on designated furniture.  Quilt is to be enlarged square one row each way.  177 more squares are made and are just enough to increase to desired size.  Determine number of small squares in original.\r<BR>\n" );
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document.write( "Not sure how to solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842996 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a good formal algebraic solution.<br><BR>\n" );
document.write( "For general problem solving, it is useful to know the result that she used to solve the problem:<br><BR>\n" );
document.write( "THE DIFFERENCE BETWEEN THE SQUARES OF CONSECUTIVE INTEGERS IS THE SUM OF THE TWO INTEGERS<br><BR>\n" );
document.write( "This is easy to see by drawing simple diagrams.  For example, consider the difference between 4^2 and 5^2.<br><BR>\n" );
document.write( "Draw a picture of a square 4 small squares on a side.<BR>\n" );
document.write( "Add 4 small squares along one side to make a 4x5 rectangle.<BR>\n" );
document.write( "Then add 5 small squares in the other direction to make the 5x5 square.<br><BR>\n" );
document.write( "So in this problem, where adding one small square on each side increases the total number of small squares by 177, we know that 177 is the sum of two consecutive integers, of which the smaller is the number of small squares on the side of the original quilt.<br><BR>\n" );
document.write( "177 = 88+89, so the original quilt was 88 squares on a side.<br><BR>\n" );
document.write( "So the number of squares in the original quilt was 88^2 = 7744.<br><BR>\n" );
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