document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011715>Question 1011715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me how to solve this problem <BR>\n" );
document.write( "\" how many numbers are there between 1 and 150 inclusive which are divisible by 5 and leave a remainder of 2 when you divide them by 3?\"<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627468 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "Question:<BR>\n" );
document.write( "How many numbers are there between 1 and 150 inclusive which are divisible by 5 and leave a remainder of 2 when you divide them by 3?<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "The number of multiples of 5 between 1 and 150 is floor(150/5)=30<BR>\n" );
document.write( "where floor(x) is the greatest integer that does not exceed x.<BR>\n" );
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document.write( "However, question requires that these multiples must leave a remainder of 2 when divided by 3.  The smallest number that satisfies this is 5, the next one is 5+(5*3)=20, where 5*3 is the product of the two factors 3 and 5.  This continues as 5+(5*3)n where n is an integer, giving 5,20,35,.... as possible candidates.<BR>\n" );
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document.write( "This will allow you to find the number of candidates required by the question.  Since you asked for the method to find it, I will leave it to you to complete the solution.<BR>\n" );
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document.write( "For more information, google \"Chinese remainder theorem\" for more explanations and examples.\r<BR>\n" );
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