Question

Solve the following real-world problem: Destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take for her account to reach $343? (1 point)
Responses

12.7 weeks
12.7 weeks

16.4 weeks
16.4 weeks

3.16 weeks
3.16 weeks

9 weeks
9 weeks

Answer 1

To solve this problem, we'll establish an equation that represents the total amount in Destiny's checking account over time.

1. **Initial deposit:** Destiny starts with $100.
2. **Weekly deposit:** She deposits $27 each week.
3. **Target amount:** She wants to reach $343.

The equation representing the amount in the checking account after \( w \) weeks can be written as follows:

\[
\text{Total amount} = 100 + 27w
\]

We need to find \( w \) when the total amount is $343:

\[
100 + 27w = 343
\]

Now, we will solve for \( w \):

1. Subtract 100 from both sides:

\[
27w = 343 - 100
\]

\[
27w = 243
\]

2. Divide both sides by 27:

\[
w = \frac{243}{27}
\]

\[
w = 9
\]

Thus, it will take Destiny **9 weeks** to reach her target of $343.

The correct response is:

**9 weeks**