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Sandy is trying to reconstruct her spending pattern from July. She knows that she had $277 in her account on July 1, but after that, her receipts and balance statements are all scrambled. Here are Sandy's records:




Date		Transaction TypeAmount (\$)

7/26		Purchase86

7/25		Deposit76

7/4		Purchase137

7/6		Deposit90

7/10		Purchase131

7/9		Purchase145

7/15		Deposit152

7/19		Purchase137






Assuming that this is a complete, if scrambled, record of Sandy's July spending and that any overdraft fees incurred do not affect the running total, how many times did Sandy overdraw her account in July?


ASandy never overdrew her account.
BSandy only overdrew her account once.
CSandy overdrew her account twice.

Verified Answer :

  • Start with an initial balance of \(\$277\).
  • Process transactions in chronological order: 7/4 (purchase), 7/6 (deposit), 7/9 (purchase), 7/10 (purchase), 7/15 (deposit), 7/19 (purchase), 7/25 (deposit), 7/26 (purchase).
  • Track the running balance: 140, 230, 85, -46, 106, -31, 45, -41.
  • Identify negative balances occurring 3 times. Final answer: \(\boxed{3}\).

Explanation

  1. Problem Analysis

To determine how many times Sandy's account balance became negative (overdrawn), we need to track her account balance chronologically. Starting with an initial balance of \(\$277\) on July 1, we apply each transaction listed in the table in the order they occurred. A deposit increases the balance, while a purchase decreases it. We define an overdraft as any instance where the balance drops below \(\$0\).

  1. Chronological Tracking of the Account Balance

First, we list the transactions chronologically and calculate the running balance at each step:

  1. Initial Balance: \(\$277\)
  2. July 4 (Purchase \(\$137\)): \(277 - 137 = \$140\)
  3. July 6 (Deposit \(\$90\)): \(140 + 90 = \$230\)
  4. July 9 (Purchase \(\$145\)): \(230 - 145 = \$85\)
  5. July 10 (Purchase \(\$131\)): \(85 - 131 = -\$46\) (First overdraft)
  6. July 15 (Deposit \(\$152\)): \(-46 + 152 = \$106\)
  7. July 19 (Purchase \(\$137\)): \(106 - 137 = -\$31\) (Second overdraft)
  8. July 25 (Deposit \(\$76\)): \(-31 + 76 = \$45\)
  9. July 26 (Purchase \(\$86\)): \(45 - 86 = -\$41\) (Third overdraft)

The balance falls below \(\$0\) on July 10, July 19, and July 26.

  1. Conclusion

Following the calculation of the running balance for each transaction, we identified three distinct dates (July 10, July 19, and July 26) where the account balance was negative. This indicates that Sandy overdrawn her account three times in total. Since the provided options (a, b, and c) are (a) never, (b) once, and (c) twice, and our calculation shows three instances, it appears there might be a discrepancy with the options; however, based strictly on the provided data and the standard definition of an overdraft, the correct count is 3. Given the format, if forced to choose the closest option, none fully describe the result, but the mathematical finding is explicitly \(\boxed{3}\).

Examples

Tracking a bank account balance is a fundamental application of simple arithmetic. By keeping a log of deposits and withdrawals, you can ensure your funds remain sufficient for your needs and avoid unnecessary overdraft fees. This practice is essential for effective personal budgeting and financial management.

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