To represent Jane's savings towards earning her bicycle, we can start with the total cost of the bike, which is $185. Jane has already received $50 for her birthday that she will put towards the bike. She plans to save an additional $15 each week until she can afford the bike.
Let \( w \) represent the number of weeks. The total amount Jane will save after \( w \) weeks can be represented as \( 15w + 50 \).
To write the equation that represents her savings equaling the cost of the bike, we set this expression equal to the total cost of the bike:
\[ 15w + 50 = 185 \]
So, the correct equation is:
15w + 50 = 185