Question

2.U.UU You have $95 in your bank account. Each week you plan to deposit $6 from your allowance and $10 from your paycheck. The equation b = 95+ (10 + 6)w gives the amount b in your account after w weeks. How many weeks from now will you have $205 in your bank account?

Answer 1

We need to find how many weeks you will have $205 in the bank account, which means that we already know b, but in this case, we have b as a function of w, then we just need to solve for w in the equation:

`95+(10+6)w=b`

We can do it like this:

1. solve the sum 10+6 inside the parentheses

`95+16w=b`

2.subtract 95 on both sides of the equation:

`\begin{gathered} 95-95+16w=b-95 \\ 16w=b-95 \end{gathered}`

3.Divide both sides by 16:

`\begin{gathered} (16w)/(16)=(b-95)/(16) \\ w=(b-95)/(16) \end{gathered}`

Now, that we have an equation to calculate w, we just have to replace b which is $205, the total amount of money that is in the bank account.

`\begin{gathered} w=(b-95)/(16) \\ w=(205-95)/(16)=(110)/(16)=6.875\approx7 \end{gathered}`

Then, we need 7 weeks to save $205 in the bank account