To find the correct equation that represents the amount of money in Sonia's savings account after \( x \) weeks, let's analyze the information given.
- Sonia opens a savings account and adds a fixed amount \( a \) every week.
- After \( T_1 \) weeks, her total savings is \( S_1 \).
- After \( T_2 \) weeks, her total savings is \( S_2 \).
The total amount in her savings account after \( x \) weeks can be represented as:
\[ y = a \cdot x + C \]
Where:
- \( y \) is the total amount in the savings account after \( x \) weeks.
- \( a \) is the amount added each week.
- \( C \) is the initial amount in the savings account.
Since we don't have specific values for \( T_1 \), \( S_1 \), \( T_2 \), and \( S_2 \) given in the problem, let's assume that:
- The amount added each week corresponds to the coefficients in the answer choices.
- The constant term corresponds to the initial amount before starting the weekly contributions.
From the choices:
- \( A: y = 7x \)
- \( B: y = 9x \)
- \( C: y = 5x + 20 \)
- \( D: y = 2x + 5 \)
The patterns suggest that \( y \) relates to the amount contributed weekly, which means that the equations consist of a linear growth based on how much Sonia adds.
If there are weekly contributions with no initial deposit, options A and B would be without a constant, which doesn't suggest any initial deposit.
For options C and D, they both have a constant added, implying there was an initial amount.
Without specific total values and weeks, we cannot definitively choose the correct equation. If you provide the values for the total amount at specific weeks or more context, we can analyze and choose the appropriate equation. If you're looking for an assumption, based on common savings patterns, \( C: y = 5x + 20 \) may imply a weekly contribution of $5 on top of a $20 initial savings, which seems reasonable for many savings account scenarios.