Question

You have ​$80 in your bank account. Each week you plan to deposit ​$8 from your allowance and ​$20 from your paycheck. The equation bequals80plus​(20plus8​)w gives the amount b in your account after w weeks. How many weeks from now will you have ​$215 in your bank​ account?

Answer 1

To find out how many weeks \( w \) it will take for your bank account balance to reach $215, you can start with the equation given:

\[
b = 80 + (20 + 8)w
\]

This simplifies to:

\[
b = 80 + 28w
\]

Now, you want to solve for \( w \) when \( b = 215 \):

\[
215 = 80 + 28w
\]

Next, subtract 80 from both sides:

\[
215 - 80 = 28w
\]
\[
135 = 28w
\]

Now, divide both sides by 28 to solve for \( w \):

\[
w = \frac{135}{28}
\]

Calculating the right side gives:

\[
w \approx 4.82
\]

Since \( w \) must be a whole number (you can't have a fraction of a week), you'll need to round up to the nearest whole number, which is 5.

Thus, it will take approximately 5 weeks to have at least $215 in your bank account. To confirm, we can plug \( w = 5 \) back into the original equation:

\[
b = 80 + 28(5)
\]
\[
b = 80 + 140
\]
\[
b = 220
\]

After 5 weeks, your bank account balance will be $220, which is sufficient. Therefore, the number of weeks it will take to reach at least $215 is:

\[
\boxed{5}
\]