SOLUTION: The average age of 30 care home residents was 77. The next day four 73 year olds move in while one resident moves out. The average age of the residents is now 76. How old was the r

Question 637357: The average age of 30 care home residents was 77. The next day four 73 year olds move in while one resident moves out. The average age of the residents is now 76. How old was the resident who moved out assuming nobody had a birthday that day.
Answer by god2012(113) (Show Source): You can put this solution on YOUR website!
Let the sum of the ages of 30 people be 'X'.
Therefore , avg age of 30 people = X/30 = 77 .
OR X = 30 * 77 = 2310
When 4 new people joins, Sum of ages = X + 4*73= 2310 + 292 = 2602.
When 1 person leaves the group, Let his age be 'Y' years
Total number of home residents = 30 + 4 -1 = 33
new average = (2602 - Y)/33 = 76.
OR Y = 2602 - (33 * 76).
Y = 94 years

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