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? 햠 Every week for 5 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. 햡 Every week for 5 weeks, deposit $20 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. 햢 Every week for 10 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday. 햣 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, we need to calculate the total deposits and withdrawals for each option over their respective time frames, starting from an initial deposit of $250.
**Option A: Every week for 5 weeks**
- Deposit: $10 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 5 weeks, total deposits = 5 weeks × 3 days/week × $10/day = 5 × 3 × 10 = $150.
- Withdraw: $27.50 on Tuesday and Thursday means 2 withdrawals per week.
- In 5 weeks, total withdrawals = 5 weeks × 2 days/week × $27.50/day = 5 × 2 × 27.50 = $275.
Net balance changes:
- Total deposits = $250 + $150 = $400.
- Total withdrawals = $275.
- Final balance = $400 - $275 = $125.
**Option B: Every week for 5 weeks**
- Deposit: $20 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 5 weeks, total deposits = 5 weeks × 3 days/week × $20/day = 5 × 3 × 20 = $300.
- Withdraw: $27.50 on Tuesday and Thursday, total withdrawals are the same as in Option A = $275.
Net balance changes:
- Total deposits = $250 + $300 = $550.
- Total withdrawals = $275.
- Final balance = $550 - $275 = $275.
**Option C: Every week for 10 weeks**
- Deposit: $10 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 10 weeks, total deposits = 10 weeks × 3 days/week × $10/day = 10 × 3 × 10 = $300.
- Withdraw: $27.50 on Tuesday and Thursday means 2 withdrawals per week.
- In 10 weeks, total withdrawals = 10 weeks × 2 days/week × $27.50/day = 10 × 2 × 27.50 = $550.
Net balance changes:
- Total deposits = $250 + $300 = $550.
- Total withdrawals = $550.
- Final balance = $550 - $550 = $0.
**Option D: Every week for 10 weeks**
- Deposit: $20 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 10 weeks, total deposits = 10 weeks × 3 days/week × $20/day = 10 × 3 × 20 = $600.
- Withdraw: The total withdrawals remain the same as above = $550.
Net balance changes:
- Total deposits = $250 + $600 = $850.
- Total withdrawals = $550.
- Final balance = $850 - $550 = $300.
**Conclusion:**
The only option that results in a zero balance is **Option C: Every week for 10 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday.**
**Option A: Every week for 5 weeks**
- Deposit: $10 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 5 weeks, total deposits = 5 weeks × 3 days/week × $10/day = 5 × 3 × 10 = $150.
- Withdraw: $27.50 on Tuesday and Thursday means 2 withdrawals per week.
- In 5 weeks, total withdrawals = 5 weeks × 2 days/week × $27.50/day = 5 × 2 × 27.50 = $275.
Net balance changes:
- Total deposits = $250 + $150 = $400.
- Total withdrawals = $275.
- Final balance = $400 - $275 = $125.
**Option B: Every week for 5 weeks**
- Deposit: $20 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 5 weeks, total deposits = 5 weeks × 3 days/week × $20/day = 5 × 3 × 20 = $300.
- Withdraw: $27.50 on Tuesday and Thursday, total withdrawals are the same as in Option A = $275.
Net balance changes:
- Total deposits = $250 + $300 = $550.
- Total withdrawals = $275.
- Final balance = $550 - $275 = $275.
**Option C: Every week for 10 weeks**
- Deposit: $10 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 10 weeks, total deposits = 10 weeks × 3 days/week × $10/day = 10 × 3 × 10 = $300.
- Withdraw: $27.50 on Tuesday and Thursday means 2 withdrawals per week.
- In 10 weeks, total withdrawals = 10 weeks × 2 days/week × $27.50/day = 10 × 2 × 27.50 = $550.
Net balance changes:
- Total deposits = $250 + $300 = $550.
- Total withdrawals = $550.
- Final balance = $550 - $550 = $0.
**Option D: Every week for 10 weeks**
- Deposit: $20 on Monday, Wednesday, and Friday means 3 deposits per week.
- In 10 weeks, total deposits = 10 weeks × 3 days/week × $20/day = 10 × 3 × 20 = $600.
- Withdraw: The total withdrawals remain the same as above = $550.
Net balance changes:
- Total deposits = $250 + $600 = $850.
- Total withdrawals = $550.
- Final balance = $850 - $550 = $300.
**Conclusion:**
The only option that results in a zero balance is **Option C: Every week for 10 weeks, deposit $10 on Monday, Wednesday, and Friday, and withdraw $27.50 on Tuesday and Thursday.**