Since the mode of the ages is 35 we know that at least two of the ages are 35. Since the range is 14 we know the third sister is not also age 35. Let x be the age of the third sister. Then we know either 35 - x = 14 or x-35 = 14 (depending if x is younger or older, respectively). Solving both of these gives x = 21 or x = 49. But all the sisters are under the age of 45, so x = 21. Hence, the ages of the sisters are
21, 35, 35.
So, the mean is (35+35+21)/3 = 91/3 =~ 30.3333 ...
