document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263246>Question 263246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I start to solve this problem?  I have tried to solve but I am so confused.\r<BR>\n" );
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document.write( "ACTIVITY 1: ISBNS AND THE CHECK DIGIT (20 points)\r<BR>\n" );
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document.write( "Each activity in this text is designed to either enhance your understanding of the topics of the preceding chapter, provide you with a mathematical extension of those topics, or both. The activities can be undertaken by one student, but they are better suited for a small group project. Occasionally it is only through discussion that different facets of the activity become apparent. For material related to this activity, visit the text website at www.mhhe.com/streeter. Have you ever noticed the long number, usually accompanied by a bar code, that can be found on the back of a book? This is called the International Standard Book Number (ISBN). Each book has a unique ISBN, which is 10 digits in length. The most common form for an ISBN is X-XX-XXXXXX-X. Each ISBN has four blocks of digits. \r<BR>\n" );
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document.write( "• The first block of digits on the left represents the language of the book (0 is used to represent<BR>\n" );
document.write( "English). This block is usually one digit in length.<BR>\n" );
document.write( "• The second block of digits represents the publisher. This block is usually two or three<BR>\n" );
document.write( "digits in length.<BR>\n" );
document.write( "• The third block of digits represents the number assigned to the book by the publishing<BR>\n" );
document.write( "company. This is usually five or six digits in length.<BR>\n" );
document.write( "• The fourth block consists of the check digit.\r<BR>\n" );
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document.write( "For the purposes of this document, we will consider the ISBN 0-07-229654-2.<BR>\n" );
document.write( "The digit of most interest is the final digit, the check digit. When an ISBN is entered<BR>\n" );
document.write( "into a computer, the computer looks at the check digit to make certain that the numbers<BR>\n" );
document.write( "were properly entered. We will look at the algorithm used to generate the check digit.\r<BR>\n" );
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document.write( "Activity<BR>\n" );
document.write( "I. To determine the check digit for the ISBN of a text, follow these steps.\r<BR>\n" );
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document.write( "1. Multiply each of the nine assigned digits by a weighted value. The weighted values<BR>\n" );
document.write( "are 1 for the first digit from the left, 2 for the second digit, 3 for third digit, etc. In our<BR>\n" );
document.write( "case, we have\r<BR>\n" );
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document.write( "1 • 0 + 2 • 0 + 3 • 7 + 4 • 2 + 5 • 2 + 6 • 9 + 7 • 6 + 8 • 5 + 9 • 4 = 211\r<BR>\n" );
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document.write( "2. In mathematics, we occasionally are interested in only the remainder after we do<BR>\n" );
document.write( "division. We refer to the remainder as the modular (or mod) of the divisor. The ISBN<BR>\n" );
document.write( "uses (mod 11) to determine the check digit.\r<BR>\n" );
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document.write( "211 ÷ 11 = 19 with a remainder of 2. We say 211 = 2 (mod 11)<BR>\n" );
document.write( "That is how we get the 2 in the ISBN 0-07-229654-2.\r<BR>\n" );
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document.write( "II. If we are given an ISBN and we want to check its validity, we can follow a similar<BR>\n" );
document.write( "algorithm.\r<BR>\n" );
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document.write( "1. Multiply each of the 10 digits by a weighted value. The weighted values are still 1 for<BR>\n" );
document.write( "the first digit from the left, 2 for the second digit, etc., but we also multiply 10 times<BR>\n" );
document.write( "the tenth (check) digit.<BR>\n" );
document.write( "In our case, we now have\r<BR>\n" );
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document.write( "1 • 0 + 2 • 0 + 3 • 7 + 4 • 2 + 5 • 2 + 6 • 9 + 7 • 6 + 8 • 5 + 9 • 4 + 10 • 2 = 231\r<BR>\n" );
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document.write( "2. For any valid ISBN, the result will have a remainder of zero when divided by 11. In<BR>\n" );
document.write( "other words, we will have 0 (mod 11). Note that 231 ÷ 11 = 21.\r<BR>\n" );
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document.write( "Determine whether each of the following is a valid ISBN.\r<BR>\n" );
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document.write( "0-07-038023-6<BR>\n" );
document.write( "0-15-249584-2<BR>\n" );
document.write( "0-553-34948-1<BR>\n" );
document.write( "0-07-000317-3\r<BR>\n" );
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document.write( "For those numbers above that are valid, go on-line and find the books to which they refer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194012 by </B><A HREF=/tutors/aboutme.mpl?userid=mducky2><B>mducky2(62)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mducky2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This looks complicated, but it's actually pretty simple. You just want to figure out which of the 4 IBSNs are valid. There are 2 ways to figure out whether an ISBN is valid, and you can use either one. <br/><br/><BR>\n" );
document.write( "<b>First Strategy</b><br/><BR>\n" );
document.write( "Let's use the first strategy with 0-07-038023-6. Except for the last digit, we're supposed to multiply all the numbers with their place in the ISBN, then add these answers up to a grand total. The 1st number is 0, the 2nd number is 0, the 3rd number is 7, and so on. <br/><BR>\n" );
document.write( "So, for the first three numbers, we'd get 1*0, 2*0, and 3*7. To do that for all the numbers looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%280%29%2B2%280%29%2B3%287%29%2B4%280%29%2B5%283%29%2B6%288%29%2B7%280%29%2B8%282%29%2B9%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+0+%2B+21+%2B+0+%2B+15+%2B+48+%2B+0+%2B+16+%2B+27 ALIGN=MIDDLE  ALT=\"0+%2B+0+%2B+21+%2B+0+%2B+15+%2B+48+%2B+0+%2B+16+%2B+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=127 ALIGN=MIDDLE  ALT=\"127\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we're supposed to divide that number by 11, and look at the remainder. Let's divide 127 by 11.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=127%2F11+=++5 ALIGN=MIDDLE  ALT=\"127%2F11+=++5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2F11 ALIGN=MIDDLE  ALT=\"+6%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means the remainder is 6 . Looking at the original ISBN, 0-07-038023-6, we see that the last number is 6. That means that the ISBN is valid!<br/><br/><BR>\n" );
document.write( "<b>Second Strategy</b><br/><BR>\n" );
document.write( "Let's use the second strategy with 0-15-249584-2. Including the last digit, we're supposed to multiply all the numbers with their place in the ISBN, then add everything to a grand total. It's basically the first strategy, plus the last digit times 10.<br/><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%280%29%2B2%281%29%2B3%285%29%2B4%282%29%2B5%284%29%2B6%289%29%2B7%285%29%2B8%288%29%2B9%284%29%2B10%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+2+%2B+15+%2B+8+%2B+20+%2B+45+%2B+35+%2B+64+%2B+36+%2B+20 ALIGN=MIDDLE  ALT=\"0+%2B+2+%2B+15+%2B+8+%2B+20+%2B+45+%2B+35+%2B+64+%2B+36+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=245 ALIGN=MIDDLE  ALT=\"245\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we're supposed to divide that number by 11. If it's a valid number, it shouldn't have any remainder.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28245%2F11%29+=+22 ALIGN=MIDDLE  ALT=\"%28245%2F11%29+=+22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F11 ALIGN=MIDDLE  ALT=\"3%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hmm. There is a remainder. It looks like this one isn't valid. <br/><br/><BR>\n" );
document.write( "That should help you get started. You can use either one of these strategies for the last two numbers, 0-553-34948-1 and 0-07-000317-3. Let me know if you need more help with the last two problems. </SPAN>\n" );
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