Respuesta :
She made an initial deposit that we will call "D", as it is one of the unknowns.
We know that she made a weekly deposit (lets call this amount "w").
After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:
[tex]D+4w=450[/tex]At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:
[tex]D+9w=825[/tex]We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.
[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]Now that we know "w", we can calculate D with any of the two equations:
[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]Answer: the initial deposit was $150.
