An orchestra consists of 25 members. The youngest member is 32 years old. She leaves and is replaced by a new member who is 30 years old.
By how much does the replacement change the average age of the members of the orchestra?
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Let A = old average and B = new average
The old average was found by dividing the sum of the ages S by 25 to get
S/25 = A
The new average is found by subtracting 32 from that sum S and adding in 30. Then you still divide by 25 (since you still have 25 people)
(S-32+30)/25 = B
(S-2)/25 = B
S/25-2/25 = B
A-2/25 = B
B = A - 2/25
B = A - 0.08
B = A - 0.08
which shows us that the average age decreased by 0.08 years