document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153223>Question 1153223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average age of players at a ten pin bowling alley increases by 1 when either four 10-year olds leave or, alternatively, if four 22-year olds arrive. How many players were there originally and what was their average age? </SPAN>\n" );
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document.write( "Let n be the number of players; let a be their average age.<br><BR>\n" );
document.write( "The sum of all their ages is na.<br><BR>\n" );
document.write( "When four 10-year-olds leave, the sum of the ages drops by 40; when that happens, the number of players decreases by 4 and the average increases by 1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=na-40+=+%28n-4%29%28a%2B1%29 ALIGN=MIDDLE  ALT=\"na-40+=+%28n-4%29%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=na-40+=+na%2Bn-4a-4 ALIGN=MIDDLE  ALT=\"na-40+=+na%2Bn-4a-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-4a+=+-36 ALIGN=MIDDLE  ALT=\"n-4a+=+-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]<br><BR>\n" );
document.write( "When four 22-year-olds join, the sum of the ages increases by 88; when that happens, the number of players increases by 4 and the average increases by 1<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=na%2B88+=+%28n%2B4%29%28a%2B1%29 ALIGN=MIDDLE  ALT=\"na%2B88+=+%28n%2B4%29%28a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=na%2B88+=+na%2Bn%2B4a%2B4 ALIGN=MIDDLE  ALT=\"na%2B88+=+na%2Bn%2B4a%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B4a+=+84 ALIGN=MIDDLE  ALT=\"n%2B4a+=+84\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<br><BR>\n" );
document.write( "Add [1] and [2]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n+=+48 ALIGN=MIDDLE  ALT=\"2n+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+24 ALIGN=MIDDLE  ALT=\"n+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute n=24 in [1] or [2] to find a=15.<br><BR>\n" );
document.write( "ANSWER: There are 24 players with an average age of 15.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "24*15 = 360; 360-40 = 320; 320/(24-4) = 320/20 = 16 -- the average age increased by 1<BR>\n" );
document.write( "24*15 = 360; 360+88 = 448; 448/(24+4) = 448/28 = 16 -- the average age increased by 1<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );