To represent Nina's savings towards earning her new phone, we need to account for the initial $100 she received and the $50 she saves each week until she reaches the total cost of the phone, which is $499.
The correct equation would be:
\[ 50w + 100 = 499 \]
This equation indicates that the total amount saved (which is $50 for each week \( w \) plus the initial $100) equals the total cost of the phone ($499).
So the correct answer is: 50w + 100 = 499.