This year, alex's grandfather's age is 6 times of Alex's age. After a few years, Alex's grandfather's age will be 5 times of Alex's age. After another few years, Alex's grandfather's age will be 4 times of Alex's age. What is Alex's grandfather's age this year?
Let grandfather’s age be G
Then Alex’ is
Let “a few years” be y. Then: Let “another few years,” or years after this year, be z. Then:
We then get:
With , ONLY MULTIPLES of 3 can be substituted for y in order to get INTEGER-VALUES for z
Therefore, if y = 3, then
This gives us: G, or the grandfather’s age as: 24(3), or 9(8) = 72.
With ONLY MULTIPLES of 3 that can be substituted for y, we substitute 6 for y to get:
This gives us: G, or the grandfather’s age as: 24(6), or 9(16) = 144
As it’s HIGHLY UNLIKELY that the grandfather is 144 years old, no LARGER multiples of 3 need to be tried/substituted.
Therefore, the more REALISTIC age for him is as stated above, 72.