Given that Brittany started by putting $209 in her account, she will deposit an additional $176 each week.
Winston made an initial deposit of $699, and he will add $127 more each week.
Let x be the number of weeks.
The equation for Brittany is

The equation for Winston is

Brittany and Winston will each have the same amount saved.
So we get B=W.
Substitute equations, we get

Subtracting 209 from both sides, we get


Subtracting 127x from both sides, we get


Dividing both sides by 49, we get


The number of weeks =10 weeks.


The amount is $1969.
Hence after 10 weeks, Brittany and Winston each have $1969 in their account.