document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169165>Question 1169165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please can assist me with the following<BR>\n" );
document.write( "Consider the intergers x and y. When y is divided by x the remainder is 29. When y is divided by x/2, the remainder is 13. Determine x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793873 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=793873\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor tried a solution by trial and error; but an arithmetic error led to an incorrect answer.<br><BR>\n" );
document.write( "A number y is divided by another number x to get a quotient of a and a remainder of b.<br><BR>\n" );
document.write( "The same number y is then divided by x/2.  There are two possible results:<br><BR>\n" );
document.write( "(a) the quotient is 2a and the remainder is again b; or<BR>\n" );
document.write( "(b) the quotient is 2a+1 and the remainder is less than b<br><BR>\n" );
document.write( "In this problem, the remainder when y is divided by x/2 is less than the remainder when it is divided by x.  That means we have the second case.<br><BR>\n" );
document.write( "y divided by x gives remainder 29:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%2B29 ALIGN=MIDDLE  ALT=\"y+=+ax%2B29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for some integer a<br><BR>\n" );
document.write( "y divided by x/2 gives remainder 13:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282a%2B1%29%28x%2F2%29%2B13 ALIGN=MIDDLE  ALT=\"y+=+%282a%2B1%29%28x%2F2%29%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Set the two expressions for y equal to each other and solve the resulting equation:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2B29+=+%282a%2B1%29%28x%2F2%29%2B13 ALIGN=MIDDLE  ALT=\"ax%2B29+=+%282a%2B1%29%28x%2F2%29%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2B29+=+ax%2Bx%2F2%2B13 ALIGN=MIDDLE  ALT=\"ax%2B29+=+ax%2Bx%2F2%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29+=+x%2F2%2B13 ALIGN=MIDDLE  ALT=\"29+=+x%2F2%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+x%2F2 ALIGN=MIDDLE  ALT=\"16+=+x%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+32 ALIGN=MIDDLE  ALT=\"x+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: x=32<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );