Solution: x =1/6x+112x+1/7x+5+1/2x+4.

x=25/28x+9

3/28x=9

x=84

This shows that Diophantu lived to the age of 84.

The second solution:

12×7=84

Answer: Because the age groups corresponding to "/12", "1/6" and "1/7" must be integers, the answer is the product of the largest coprime factors in "12", "6" and "7".