Question 1153223
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Let n be the number of players; let a be their average age.<br>
The sum of all their ages is na.<br>
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>
{{{na-40 = (n-4)(a+1)}}}
{{{na-40 = na+n-4a-4}}}
{{{n-4a = -36}}}  [1]<br>
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>
{{{na+88 = (n+4)(a+1)}}}
{{{na+88 = na+n+4a+4}}}
{{{n+4a = 84}}}  [2]<br>
Add [1] and [2]:<br>
{{{2n = 48}}}
{{{n = 24}}}<br>
Substitute n=24 in [1] or [2] to find a=15.<br>
ANSWER: There are 24 players with an average age of 15.<br>
CHECK:
24*15 = 360; 360-40 = 320; 320/(24-4) = 320/20 = 16 -- the average age increased by 1
24*15 = 360; 360+88 = 448; 448/(24+4) = 448/28 = 16 -- the average age increased by 1<br>