To solve the equation \( 100 + 27w = 343 \) for \( w \), follow these steps:
- Subtract 100 from both sides of the equation:
\[ 27w = 343 - 100 \]
\[ 27w = 243 \]
- Now, divide both sides by 27 to solve for \( w \):
\[ w = \frac{243}{27} \]
- Perform the division:
\[ w = 9 \]
So, it will take Destiny 9 weeks to reach $343 in her checking account.