Answer:
49
Step-by-step explanation:
The differences of the given ages from the new mean are ...
-2, -10, -8, -2, -2
The sum of these is -24. In order to make the total of differences from the mean be zero, the new person entering the room must be 24 years older than the new mean, so must be 25 +24 = 49.
The person who entered is 49 years old.
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Comment on the solution method
I find it easiest to work problems like this in the manner described above. It works on the idea that adding or subtracting the same value from every number changes the mean by that value. That is, if I subtract 25 from every person's age in the room, the mean of that set of differences will be 25 less than the mean, so will be 25 -25 = 0.
I know the mean of those differences will be zero if their sum is zero. I find it easier to add some small numbers, rather than deal with multiplying or dividing the sum of larger numbers.
