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 how much was Latoya adding to her account each week , and what was her intial deposit.

Answer 1

Let the initial deposite in the savings account be U.

Also, let the amount Latoya adds each week to the savings account be V.

That is, after first week, Latoya has U + V;

Similarly after second week, Latoya has U + 2V;

Then, after fourth week, Latoya has U + 4V

and after ninth week, Latoya has U + 9V

`\begin{gathered} So, \\ U+4V=450\ldots\ldots.\ldots\ldots equation\text{ 1} \\ U+9V=825\ldots\ldots\ldots\ldots.equation\text{ 2} \\ \text{equation 2 - equation 1} \\ 9V-4V=825-450 \\ 5V=375 \\ V=(375)/(5) \\ V=75 \end{gathered}`

Hence, the amount Latoya add each week to the savings account is $75.

Also,

`\begin{gathered} Put\text{ V=75 in equation 1} \\ U+4V=450 \\ U+4(75)=450 \\ U+300=450 \\ U=450-300 \\ U=150 \end{gathered}`

Thus, the initial deposit in the savings account is $150.