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
[tex]B=209+176x[/tex]The equation for Winston is
[tex]W=699+127x[/tex]Brittany and Winston will each have the same amount saved.
So we get B=W.
Substitute equations, we get
[tex]209+176x=699+127x[/tex]Subtracting 209 from both sides, we get
[tex]209+176x-209=699+127x-209[/tex][tex]176x=127x+490[/tex]Subtracting 127x from both sides, we get
[tex]176x-127x=127x+490-127x[/tex][tex]49x=490[/tex]Dividing both sides by 49, we get
[tex]\frac{49x}{49}=\frac{490}{49}[/tex][tex]x=10[/tex]The number of weeks =10 weeks.
[tex]\text{ Substitute x=10 in 209+176x, we get}[/tex][tex]209+176(10)=209+1760=1969[/tex]The amount is $1969.
Hence after 10 weeks, Brittany and Winston each have $1969 in their account.