To determine how many weeks it will take for Destiny's checking account to reach $343, we can set up the following equation.
Initially, she has $100 in her account, and she deposits $27 each week. Let \( w \) represent the number of weeks. The total amount in her account after \( w \) weeks can be represented as:
\[ \text{Total amount} = 100 + 27w \]
We want to find \( w \) when the total amount reaches $343:
\[ 100 + 27w = 343 \]
Now, we can solve for \( w \):
- Subtract 100 from both sides:
\[ 27w = 343 - 100 \] \[ 27w = 243 \]
- Divide both sides by 27:
\[ w = \frac{243}{27} \] \[ w = 9 \]
Thus, it will take Destiny 9 weeks for her account to reach $343.