To find the amount Nina has saved after \( w \) weeks, we start with the $100 she received for her birthday and add the amount she saves each week, which is $50 multiplied by the number of weeks \( w \). Therefore, the total savings equation is:
\[ 50w + 100 = 499 \]
So, the correct response is:
50w + 100 = 499
(50 w plus 100 is equal to 499)