Problem: Al's age is 16 more than the sum of Bob's age and Carl's age, and the square of Al's age is 1632 more than the square of the sum of Bob's age and Carl's age. The sum of the ages of Al,Bob and Carl is
Answer Choices:
A. 64
B. 94
C. 96
D. 102
E. 140
Solution:
Let a,b and c denote Al's age, Bob's age and Carl's age, respectively. Then
a+b+c​=a−(b+c)(a+b+c)(a−(b+c))​=a−(b+c)a2−(b+c)2​=161632​=102​