document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=441801>Question 441801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im a 9th grade student and I usually have no problem with word problems(even algebraic ones), but there is one problem which I have difficulty with;\r<BR>\n" );
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document.write( "A certain number of matches are needed to fill 24 boxes, with each box containing the same number of matches. When 4 less matches are put into each box there are enough for 28 boxes. Find the total number of matches.\r<BR>\n" );
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document.write( "I just need to form an equation and the rest can be solved by me\r<BR>\n" );
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document.write( "I tried \"24(x-4) = 28x\" but that didnt help!<BR>\n" );
document.write( "Any help would be appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304831 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=304831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A certain number of matches are needed to fill 24 boxes, with each box containing the same number of matches. When 4 less matches are put into each box there are enough for 28 boxes. Find the total number of matches. <BR>\n" );
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document.write( "Let \"x\" be the total number of matches.<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "x = 28k + 4 where k is some positive integer.<BR>\n" );
document.write( "x = 24p where p = is some positive integer<BR>\n" );
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document.write( "24p = 28k+4<BR>\n" );
document.write( "6p = 7k +1<BR>\n" );
document.write( "7k-6p = -1<BR>\n" );
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document.write( "Integer solution: 6*6= 7*5 -1<BR>\n" );
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document.write( "k = 5 when p = 6<BR>\n" );
document.write( "Then x = 24p = 144 matches<BR>\n" );
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document.write( "Other solutions:<BR>\n" );
document.write( "k = 17 when p = 20<BR>\n" );
document.write( "or<BR>\n" );
document.write( "k = 35 when p = 41<BR>\n" );
document.write( "or<BR>\n" );
document.write( "k = 47 when p = 55<BR>\n" );
document.write( "etc.<BR>\n" );
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document.write( "I used a graphing calculator to find these <BR>\n" );
document.write( "solutions on the \"Table\" after entering<BR>\n" );
document.write( "y = (7x+1)/6  in the \"Y=\" list.  Sometimes<BR>\n" );
document.write( "just knowing the solutions have to be Real,<BR>\n" );
document.write( "or Integer, or Natural numbers is the key<BR>\n" );
document.write( "clue to the solution.  Your equation would<BR>\n" );
document.write( "result in the same answers I found.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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