Questions: Ronald is trying to reconstruct his spending pattern from May. He knows that he had 315 in his account on May 1, but after that, his receipts and balance statements are all scrambled. Here are Ronald's records: Date Transaction Type Amount () 5 / 25 Purchase 66 5 / 18 Purchase 90 5 / 30 Purchase 188 5 / 24 Deposit 151 5 / 22 Purchase 152 5 / 8 Deposit 104 5 / 3 Purchase 175 5 / 6 Purchase 82 Assuming that this is a complete, if scrambled, record of Ronald's May spending and that any overdraft fees incurred do not affect the running total, how many times did Ronald overdraw his account in May?

Solution Steps

To determine how many times Ronald overdrew his account, we need to simulate his account balance throughout May by processing each transaction in chronological order. We start with the initial balance and apply each transaction, checking if the balance goes below zero after each transaction.

Ronald starts with an initial balance of \( B_0 = 315 \).

We process each transaction in chronological order:

1. Purchase on May 3: \[ B_1 = B_0 - 175 = 315 - 175 = 140 \]

2. Purchase on May 6: \[ B_2 = B_1 - 82 = 140 - 82 = 58 \]

3. Deposit on May 8: \[ B_3 = B_2 + 104 = 58 + 104 = 162 \]

4. Purchase on May 18: \[ B_4 = B_3 - 90 = 162 - 90 = 72 \]

5. Purchase on May 22: \[ B_5 = B_4 - 152 = 72 - 152 = -80 \] (First overdraft occurs here)

6. Deposit on May 24: \[ B_6 = B_5 + 151 = -80 + 151 = 71 \]

7. Purchase on May 25: \[ B_7 = B_6 - 66 = 71 - 66 = 5 \]

8. Purchase on May 30: \[ B_8 = B_7 - 188 = 5 - 188 = -183 \] (Second overdraft occurs here)

Ronald overdrew his account twice during the month of May.

Final Answer