To find the equation that represents Nina's savings, we start by noting that she has $100 from her birthday. Then, she plans to save $50 for each week, which we will represent with the variable \( w \) for the number of weeks.
The total amount Nina will have saved after \( w \) weeks is \( 50w + 100 \).
Since she needs a total of $499 to purchase the phone, we can set up the equation:
\[ 50w + 100 = 499. \]
So the correct response is:
50w + 100 = 499.