Question
. Ann opened a new savings account with an initial deposit of $250. Which combination will result in a zero balance in Ann’s account? a Every week for 5 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. b Every week for 5 weeks, deposit $20 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. c Every week for 10 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. d Every week for 10 weeks, deposit $20 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday.
Answers
GPT-4o mini
To determine which combination will result in a zero balance in Ann’s account, let's calculate the total deposits and withdrawals for each option.
**Initial Deposit: $250**
### Option a:
- **Deposits:**
- $10 on Monday, Wednesday, and Friday for 5 weeks:
\(3 \text{ days/week} \times 5 \text{ weeks} \times 10 \text{ dollars} = 150 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 5 weeks:
\(2 \text{ days/week} \times 5 \text{ weeks} \times 27.50 \text{ dollars} = 275 \text{ dollars}\)
- **Total after 5 weeks:**
\[
250 \text{ (initial)} + 150 \text{ (deposits)} - 275 \text{ (withdrawals)} = 125 \text{ dollars}
\]
### Option b:
- **Deposits:**
- $20 on Monday, Wednesday, and Friday for 5 weeks:
\(3 \text{ days/week} \times 5 \text{ weeks} \times 20 \text{ dollars} = 300 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 5 weeks:
\(2 \text{ days/week} \times 5 \text{ weeks} \times 27.50 \text{ dollars} = 275 \text{ dollars}\)
- **Total after 5 weeks:**
\[
250 \text{ (initial)} + 300 \text{ (deposits)} - 275 \text{ (withdrawals)} = 275 \text{ dollars}
\]
### Option c:
- **Deposits:**
- $10 on Monday, Wednesday, and Friday for 10 weeks:
\(3 \text{ days/week} \times 10 \text{ weeks} \times 10 \text{ dollars} = 300 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 10 weeks:
\(2 \text{ days/week} \times 10 \text{ weeks} \times 27.50 \text{ dollars} = 550 \text{ dollars}\)
- **Total after 10 weeks:**
\[
250 \text{ (initial)} + 300 \text{ (deposits)} - 550 \text{ (withdrawals)} = 0 \text{ dollars}
\]
### Option d:
- **Deposits:**
- $20 on Monday, Wednesday, and Friday for 10 weeks:
\(3 \text{ days/week} \times 10 \text{ weeks} \times 20 \text{ dollars} = 600 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 10 weeks:
\(2 \text{ days/week} \times 10 \text{ weeks} \times 27.50 \text{ dollars} = 550 \text{ dollars}\)
- **Total after 10 weeks:**
\[
250 \text{ (initial)} + 600 \text{ (deposits)} - 550 \text{ (withdrawals)} = 300 \text{ dollars}
\]
### Conclusion:
The only option that results in a zero balance in Ann's account is **Option c**.
**Initial Deposit: $250**
### Option a:
- **Deposits:**
- $10 on Monday, Wednesday, and Friday for 5 weeks:
\(3 \text{ days/week} \times 5 \text{ weeks} \times 10 \text{ dollars} = 150 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 5 weeks:
\(2 \text{ days/week} \times 5 \text{ weeks} \times 27.50 \text{ dollars} = 275 \text{ dollars}\)
- **Total after 5 weeks:**
\[
250 \text{ (initial)} + 150 \text{ (deposits)} - 275 \text{ (withdrawals)} = 125 \text{ dollars}
\]
### Option b:
- **Deposits:**
- $20 on Monday, Wednesday, and Friday for 5 weeks:
\(3 \text{ days/week} \times 5 \text{ weeks} \times 20 \text{ dollars} = 300 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 5 weeks:
\(2 \text{ days/week} \times 5 \text{ weeks} \times 27.50 \text{ dollars} = 275 \text{ dollars}\)
- **Total after 5 weeks:**
\[
250 \text{ (initial)} + 300 \text{ (deposits)} - 275 \text{ (withdrawals)} = 275 \text{ dollars}
\]
### Option c:
- **Deposits:**
- $10 on Monday, Wednesday, and Friday for 10 weeks:
\(3 \text{ days/week} \times 10 \text{ weeks} \times 10 \text{ dollars} = 300 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 10 weeks:
\(2 \text{ days/week} \times 10 \text{ weeks} \times 27.50 \text{ dollars} = 550 \text{ dollars}\)
- **Total after 10 weeks:**
\[
250 \text{ (initial)} + 300 \text{ (deposits)} - 550 \text{ (withdrawals)} = 0 \text{ dollars}
\]
### Option d:
- **Deposits:**
- $20 on Monday, Wednesday, and Friday for 10 weeks:
\(3 \text{ days/week} \times 10 \text{ weeks} \times 20 \text{ dollars} = 600 \text{ dollars}\)
- **Withdrawals:**
- $27.50 on Tuesday and Thursday for 10 weeks:
\(2 \text{ days/week} \times 10 \text{ weeks} \times 27.50 \text{ dollars} = 550 \text{ dollars}\)
- **Total after 10 weeks:**
\[
250 \text{ (initial)} + 600 \text{ (deposits)} - 550 \text{ (withdrawals)} = 300 \text{ dollars}
\]
### Conclusion:
The only option that results in a zero balance in Ann's account is **Option c**.