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

12.7 weeks
12.7 weeks

3.16 weeks
3.16 weeks

16.4 weeks

Answer 1

To solve the problem, we need to find out how many weeks (let's call this \( w \)) it will take for Destiny's checking account to reach $343, starting with an initial deposit of $100 and making weekly deposits of $27.

We can set up the equation as follows:

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

Plugging in the known values:

\[ 343 = 100 + 27w \]

Now we will solve for \( w \):

1. Subtract 100 from both sides:

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

2. Divide both sides by 27:

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

Calculating this gives:

\[ w = 9 \]

So, it will take Destiny 9 weeks for her account to reach $343.

Thus, the correct response is:

9 weeks.