Answer:
Tanya is 18 years old.
Step-by-step explanation:
In order to determine this, we assume the following
x = tens digit of the age of Tanya, and also the hundreds digit of Tanya's great-grandfather age
y = units digit of the age of Tanya, and also the units digit of Tanya's great-grandfather age
Therefore, we have:
10x + y = (1 / 6) * (100x + y)
Multiply both sides by 6, we have:
[10x + y] * 6 = [(1 / 6) * (100x + y)] * 6
60x + 6y = 100x + y
Collect the like terms, we have:
6y - y = 100x - 60x
5y = 40x
Divide through by 5, we have:
y = 8x
That is,
8x = y
Note that x and y has to be single digits. This can only be obtained only when x = 1 and y = 8. And given how x and y is defined above, we have:
The age of Tanya = 18
This can be verified as follows:
18 = 108 / 6
18 * 6 = 108
108 = 108
Therefore, Tanya is 18 years old.
