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?

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HuzaifahS22024 HuzaifahS22024

29-10-2022
Mathematics

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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?

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BerklyT253656 BerklyT253656 · Answer 1 · 2022-10-29T09:56:30+02:00

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:

[tex]95+(10+6)w=b[/tex]

We can do it like this:

1. solve the sum 10+6 inside the parentheses

[tex]95+16w=b[/tex]

2.subtract 95 on both sides of the equation:

[tex]\begin{gathered} 95-95+16w=b-95 \\ 16w=b-95 \end{gathered}[/tex]

3.Divide both sides by 16:

[tex]\begin{gathered} \frac{16w}{16}=\frac{b-95}{16} \\ w=\frac{b-95}{16} \end{gathered}[/tex]

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.

[tex]\begin{gathered} w=\frac{b-95}{16} \\ w=\frac{205-95}{16}=\frac{110}{16}=6.875\approx7 \end{gathered}[/tex]

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