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)

Question

Responses

9 weeks
9 weeks

3.16 weeks
3.16 weeks

12.7 weeks
12.7 weeks

16.4 weeks
16.4 weeks

Answer 1

To determine how many weeks it will take for Destiny's checking account to reach $343, we can set up an equation based on her initial deposit and weekly contributions.

1. Starting amount = $100
2. Weekly deposit = $27
3. Target amount = $343

Let \( w \) represent the number of weeks. The total amount in Destiny's account after \( w \) weeks can be expressed as:

\[ \text{Total Amount} = \text{Initial Deposit} + (\text{Weekly Deposit} \times \text{Number of Weeks}) \]

This can be formulated as:

\[ 100 + 27w = 343 \]

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

1. Subtract 100 from both sides:

\[ 27w = 343 - 100 \] \[ 27w = 243 \]

2. Divide both sides by 27:

\[ w = \frac{243}{27} = 9 \]

Therefore, it will take Destiny 9 weeks to reach a balance of $343 in her checking account.

The correct response is 9 weeks.