Question

I need to make sure some of my awnsers are correct

Answer 1

We need to find the number of weeks (w) it will take for their account ballance to be equal. We first need to create equations for each person.

Rhianon has a balance of "-$253.50" at the start and she'll add "$35.80" per week. This means that the balance on her account as a function of the weeks is:

`\text{rhianon}=35.8\cdot w-253.5`

We need to subtract her depositis by the initial balance of the account.

Sophie has a balance of "-$78.25" and she'll deposit "$23.3" every week. We will do the same as before to find the expression. We have:

`\text{sophie}=23.3\cdot w-78.25`

We need to find the number of weeks that it will take before their accounts have the same ballance. When this happens the two expressions must be equal, therefore:

`\begin{gathered} \text{rhianon=sophie} \\ 35.8w-253.5=23.3\cdot w-78.25 \\ \end{gathered}`

We need to isolate the "w" variable on the left side. To do that we will change the other termos from one side to the other, when that happens their signals get inverted.

`\begin{gathered} 35.8w-23.3w=253.5-78.25 \\ 12.5w=175.25 \end{gathered}`

Now we need to divide both sides by 12.5

`\begin{gathered} (12.5)/(12.5)w=(175.25)/(12.5) \\ w=14.02 \end{gathered}`

It will take approximately 14 weeks until their ballance is equal.