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

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