SOLUTION: 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

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Question 1153223: 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?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let n be the number of players; let a be their average age.

The sum of all their ages is na.

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:

na-40+=+%28n-4%29%28a%2B1%29
na-40+=+na%2Bn-4a-4
n-4a+=+-36 [1]

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

na%2B88+=+%28n%2B4%29%28a%2B1%29
na%2B88+=+na%2Bn%2B4a%2B4
n%2B4a+=+84 [2]

Add [1] and [2]:

2n+=+48
n+=+24

Substitute n=24 in [1] or [2] to find a=15.

ANSWER: There are 24 players with an average age of 15.

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