To solve the problem, we can set up an equation. Destiny starts with $100 and deposits $27 each week. We want to find out how many weeks it will take for her account to reach $343.
Let \( w \) be the number of weeks. The total amount in her account after \( w \) weeks can be represented by the equation:
\[ 100 + 27w = 343 \]
Now, we need to solve for \( w \):
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Subtract 100 from both sides: \[ 27w = 343 - 100 \] \[ 27w = 243 \]
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Divide both sides by 27: \[ w = \frac{243}{27} \] \[ w = 9 \]
It will take Destiny 9 weeks for her account to reach $343.
Therefore, the correct response is 9 weeks.