Math question on Ratios problem solving

Question

The ratio of the age of Bob to her mother in 2001 was 1:11

The ratio of the age of Bob to her mother in 2018 was 2:5

What will be the ratio of Bob's age to her mother in 2030?

Answer 1

Let x = Bob's age in 2001. So the mother is 11x (in 2001)

In 2018, 17 years later (so Bob is x+17 and mother is 11x+17) is 2:5 So 5(x+17) = 2(11x+17)

We can solve this last equation for x

5x+85 = 22x +34, so 17x = 51 and x=3

So in 2001 Bob is 3 and mother is 33

In 2030, 29 years after 2001, Bob will be 32 and his mother will be 62. So their ratio will be 32:62 or 16:31