Question

Latoya opened a savings account and made an intial deposit. After the intial deposit, she added money into the account each week she added the same amount each week with out any withdrawals after the forth week she had $450 by the ninth week she had $825 what was latoya's intial deposit?

Answer 1

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:

`D+4w=450`

At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:

`D+9w=825`

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.

`\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=(375)/(5) \\ w=75 \end{gathered}`

Now that we know "w", we can calculate D with any of the two equations:

`\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}`

Answer: the initial deposit was $150.