There is one unknown in this problem — how much cigarettes in one pack. I suppose this is 20, but let's denote this quantity as `n_p` .
During a week, a person smokes `10*n_p` cigarettes. Each cigarette contains 5 mg of tar so `10*n_p` cigarettes contain
`50*n_p` mg of tar = `0.05*n_p` g of tar (by week).
One lb is approx. 454g, so 0.25lb is 0.25*454 = 113.5 (g).
Now, divide the "desired" quantity of tar by its "speed" to obtain time:
`(113.5)/(0.05*n_p) = 2270/n_p` (weeks).
For `n_p=20` then `0.05*n_p=1` (g) and the answer is 113.5 weeks, or slightly more than 2 years.
For `n_p=25` the answer is 2270/25=90.8 (weeks).
You can compute the answer for any given `n_p.`