document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205868>Question 1205868</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, So my question is: <BR>\n" );
document.write( "A bag of lollies is shared. When shared equally among 4 people, there are 2 lollies left. When shared equally among 9 people, there are 5 lollies left. When shared equally among 7 people, there are 2 lollies left.<BR>\n" );
document.write( "Determine the smallest possible number of lollies that could have been in the bag as well as the general solution.<BR>\n" );
document.write( "I have tried a few different ways and get different answers.I either get 86 or 94. Can you help? Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842937 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A bag of lollies is shared. When shared equally among 4 people, there are 2 lollies left. <BR>\n" );
document.write( "When shared equally among 9 people, there are 5 lollies left. When shared equally among 7 people, <BR>\n" );
document.write( "there are 2 lollies left.<BR>\n" );
document.write( "Determine the smallest possible number of lollies that could have been in the bag as well as the general solution.<BR>\n" );
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document.write( "86 is the correct answer, as you can easily check it &nbsp;ON &nbsp;YOUR &nbsp;OWN.\r<BR>\n" );
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document.write( "94 is incorrect answer, as you can easily check it &nbsp;ON &nbsp;YOUR &nbsp;OWN.\r<BR>\n" );
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document.write( "I do not understand, why do you panic, having a correct answer in your hands.\r<BR>\n" );
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document.write( "You always can easily check it &nbsp;ON &nbsp;YOUR &nbsp;OWN &nbsp;if the answer is correct or not,<BR>\n" );
document.write( "if you do understand correctly the meaning of the problem.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Edwin presented huge long solution, which may scare you.<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Therefore, &nbsp;I decided to post here my solution, &nbsp;which is a standard method <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for such problems and is much shorter.\r<BR>\n" );
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document.write( "Let N be our number.\r\n" );
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document.write( "Subtract 2 from N and consider the number N-2.\r\n" );
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document.write( "Since N gives the remainder 2 when is divided by 4 and by 7, we conclude that \r\n" );
document.write( "the number (N-2) is divided by 4 and by 7 with no remainder.\r\n" );
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document.write( "Hence, N-2 is divided by 4*7 = 28  (since 4 and 7 are relatively prime numbers).\r\n" );
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document.write( "So, we can write  N-2 = 28k,  where \"k\" is some integer number.\r\n" );
document.write( "Hence,  N = 28k + 2.\r\n" );
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document.write( "Therefore, we will consider the numbers of the form 28k+2 to find value of \"k\" such \r\n" );
document.write( "that 28k+2 gives the remainder 5 when is divided by 9.\r\n" );
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document.write( "Try some values k= 1, 2, 3, 4, 5 . . . .\r\n" );
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document.write( "It will not take long time, since k=3 just provides you the number N= 28*3+2 = 86,\r\n" );
document.write( "which gives the remainder 5 when is divided by 9.\r\n" );
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document.write( "So, the number 86 is the <U>ANSWER</U>.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "If you want to see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/divisibility/The-number-rem4-mod7-rem5-mod8-and-rem6-mod9.lesson>The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9</A> \r<BR>\n" );
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document.write( "in this site. \r<BR>\n" );
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document.write( "These problems are typical for this subject, and reading these lessons,<BR>\n" );
document.write( "you will get familiar with the basic methods.\r<BR>\n" );
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document.write( "Problems of this type are introductory into the subject on divisibility and remainders.\r<BR>\n" );
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document.write( "In advanced Math circles/classes, students start learning this material at 4th grade.<BR>\n" );
document.write( "May be, it is too early, but learning it, let say, at 5th - 6th grade is just good time.\r<BR>\n" );
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document.write( "It is absolutely clear that 4th, 5th and even 6th grade student is not able to perceive long reasoning.\r<BR>\n" );
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document.write( "But such a student should be able to easy perceive what is written in my post - it is why I wrote it here.\r<BR>\n" );
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document.write( "Since Edwin continue this discussion, I'd like to answer on his very first point.\r<BR>\n" );
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document.write( "Edwin writes that \"Ikleyn believes trial and error is legitimate, but it isn't!\".\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- No.  &nbsp;&nbsp;It is not so.\r<BR>\n" );
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document.write( "What I state is another statement: \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\"If trial and error produces the answer, which after checking <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is proven to be correct, then the answer is correct <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the solution is legitimate.\"\r<BR>\n" );
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document.write( "Edwin, it is not a good style to make a discussion<BR>\n" );
document.write( "by attributing me statements that I did not make,<BR>\n" );
document.write( "and then disproving these statements.\r<BR>\n" );
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document.write( "Such method of making discussion was known back in ancient Greece,<BR>\n" );
document.write( "and it has the name - which I do not want to pronounce here.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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