It definitely depends on your time frame but yes, it will save her money. Considering three years, she would save almost 500 dollars.
Janie drinks 84.5 ounces (0.6 gallons) of water each day, so the 24-pack will last her almost five days at the price of three dollars. If we give ourselves the time frame of 3 years, it will cost about 675 dollars (225 a year) to maintain her hydration with non-reusable bottles.
y= (4.8 times x/5) times 3.09
For reference, Janie would drink 657 gallons of water over these three years
The filter and bottle cost 38 dollars combined, and she would need three packages of the refill filters for 99 dollars. It would cost her 137 dollars to drink reusable for these 3 years.