You have ​$60 in your bank account. Each week you plan to deposit ​$9 from your allowance and ​$25 from your paycheck. The equation bequals60plus​(25plus9​)w gives the amount b in your account after w weeks. How many weeks from now will you have ​$225 in your bank​ account?

Answer 1

To find out how many weeks it will take for your bank account to reach $225, we can start with the equation provided:

\[ b = 60 + (25 + 9)w \]

This simplifies to:

\[ b = 60 + 34w \]

Here, \( b \) is the amount in your bank account after \( w \) weeks, and \( 34 \) is the total amount you deposit each week (since \( 25 + 9 = 34 \)).

Next, we want to find out when \( b \) will be equal to \( 225 \):

\[ 225 = 60 + 34w \]

Now, subtract \( 60 \) from both sides to isolate the term with \( w \):

\[ 225 - 60 = 34w \]

This gives us:

\[ 165 = 34w \]

Next, divide both sides by \( 34 \) to solve for \( w \):

\[ w = \frac{165}{34} \approx 4.85 \]

Since \( w \) represents weeks, we need a whole number. Therefore, it will take approximately 5 weeks to reach or exceed $225 in your account.

Let's verify:

• After 4 weeks: \[ b = 60 + 34 \times 4 = 60 + 136 = 196 \]

• After 5 weeks: \[ b = 60 + 34 \times 5 = 60 + 170 = 230 \]

Thus, in 5 weeks, you will have $230, which exceeds $225. Therefore, it will take 5 weeks to have at least $225 in your bank account.