Let n be the number of months Ms. Gray will need to save $4,189, then we can set the following equation:
[tex]4,189=60n\text{.}[/tex]Dividing the above equation by 60 we get:
[tex]\begin{gathered} \frac{4189}{60}=n, \\ n\approx69.82. \end{gathered}[/tex]Since n must be a whole number, then Ms. Gray needs at least 70 months to save enough to buy a new television.
Answer: 70 months.