document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190068>Question 1190068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In school , the ratio of the number of pupils to the number of teachers is exactly 19.6:1 .<BR>\n" );
document.write( "a) find the smallest possible number of pupils in the school.<BR>\n" );
document.write( "b) the total number of teachers and pupils in the school is in fact 927 . find the number of teachers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821629 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ratio of the number of pupils to the  number of teachers is exactly 19.6:1.<BR>\n" );
document.write( "multiply both sides of this ratio by 10 to get 196:10.<BR>\n" );
document.write( "this ratio can be simplified to 98:5, which are still whole numbers.<BR>\n" );
document.write( "the total number of teachers and pupils in the school can't be less than 103 because you would then get a fractional part of a student or teacher which is not possible.<BR>\n" );
document.write( "given that 103 is the minimum number of students and pupils, then, if the total number of students and pupil is 927, then divided 927 by 103 to get 9 sets of 103.<BR>\n" );
document.write( "the number of pupils would be 9 * 98 = 882 and the number of teachers would be 9 * 5 = 45.<BR>\n" );
document.write( "882 + 45 = 927 total.\r<BR>\n" );
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document.write( "if you let x equal a factor of the total, then you get:<BR>\n" );
document.write( "19.6 * x + 1 * x = 20.6 * x.<BR>\n" );
document.write( "you are looking for the smallest amount of x to make the total an integer.<BR>\n" );
document.write( "in fact, you are looking for the smallest amount of x to make .6 an integer.<BR>\n" );
document.write( "the smallest amount of x is 5 because .6 * 5 = 3.<BR>\n" );
document.write( "therefore, 19.6 * x + 1 * x = 20.6 * x becomes 19.6 * 5 + 1 * 5 = 20.6 * 5.<BR>\n" );
document.write( "this results in 98 + 5 = 103.<BR>\n" );
document.write( "any amount of pupils and students less than that will not result in a whole number.<BR>\n" );
document.write( "927 / 103 = 9 sets of 98 students and 5 teachers.<BR>\n" );
document.write( "that becomes a total of 9 * 98 = 882 students and 9 * 5 = 45 teachers for a total of 882 + 45 = 927 students and teachers.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo<BR>\n" );
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