document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102691>Question 1102691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average age of boys in a class of 30 is 15 years. If 10 more boys join the class, the average of the whole class gets reduced by a year. What is the average age of newcomers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717421 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717421\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "... and here is another solution using logical analysis -- similar to, yet very different from -- tutor ikleyn's second solution.<br><BR>\n" );
document.write( "This is a method I like to use when a problem is about averages of numbers that are all \"close together\".<br><BR>\n" );
document.write( "The average of the 30 boys originally in the class is 15.<br><BR>\n" );
document.write( "After the 10 new boys join the class, the average of all 40 boys is 14; the average age went down by 1 year.<br><BR>\n" );
document.write( "On average, each of the 30 boys originally in the class is 1 year older than the new average; that means all together their ages are a total of 30 more than what is needed to make the new average.<br><BR>\n" );
document.write( "The total of the ages of the 10 new boys has to balance out those 30 \"extra\" years from the original 30 boys; that means the average age of the 10 new boys has to be 30/10 = 3 years LESS than the new average.<br><BR>\n" );
document.write( "Since the new average is 14, the average age of the 10 new boys is 14-3 = 11.<br><BR>\n" );
document.write( "With practice, this solution method is easy to use.  We can see how the method works by representing it symbolically, like this:<br><BR>\n" );
document.write( "(1) Let A be the new average.<BR>\n" );
document.write( "(2) The sum of the ages of the original 30 boys in the class is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%28A%2B1%29+=+30A%2B30 ALIGN=MIDDLE  ALT=\"30%28A%2B1%29+=+30A%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(3) The new average, with 40 boys, is A; you want the total of the ages of all 40 boys to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40A ALIGN=MIDDLE  ALT=\"40A\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(4) From (2) and (3), we see that the total of the ages of the 10 new boys has to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40A+-+%2830A%2B30%29+=+10A-30 ALIGN=MIDDLE  ALT=\"40A+-+%2830A%2B30%29+=+10A-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "(5) And that means the average age of the 10 new boys must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810A-30%29%2F10+=+A-3 ALIGN=MIDDLE  ALT=\"%2810A-30%29%2F10+=+A-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And since the new average is 14, the average age of the 10 new boys is 14-3 = 11. </SPAN>\n" );
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