9. Three sisters, whose average age is 10 , all have different ages. The average age of one pair of the sisters is 11 , while the average age of a different pair is 12 . What is the age of the eldest sister?
A 10
B 11
С 12
D 14
E 16
Solution
$\mathbf{E}$

Since the average age of the three sisters is 10 , their total age is $3 \times 10=30$.
Since the average age of one pair of the sisters is 11 , their total age is $2 \times 11=22$ and hence the age of the sister not included in that pairing is $30-22=8$. Similarly, since the average age of a different pair of sisters is 12 , their total age is $2 \times 12=24$ and hence the age of the sister not included in that pairing is $30-24=6$. Therefore the age of the eldest sister is $30-8-6=16$.