When Grandma was asked about her age she told her grandchildren the following:
-"If the age of the oldest of you will be added to the product of ages of the younger two,- you would get my current age."
The three boys, Alex, Bob and Cid, started their thinking, but only Bob, the middle child provided the correct answer and added:
"If we had to perform the above operations a year ago - we would be off by 14 years...
What were the boys' Grandma's ages, given Alex's age was a prime number?

We're not told whether Alex is the youngest or oldest. 

Anyway, let's call the children a, b, and c in order from youngest to oldest.  We have two equations:

[1] ab + c = G

ab = G - c

[2] (a-1)(b-1) + (c-1) = G - 15

ab - a - b + c = G - 15

ab - a - b + 15 = G - c

Therefore

ab = ab - a - b + 15

So we have

a + b = 15

which agrees with what Charlie found.  This allows for many possible solutions, both where the youngest age is prime or the oldest age is prime. 

Edited on August 20, 2014, 4:36 pm

Posted by tomarken on 2014-08-20 16:33:12