Ted is looking over his spending pattern for the past week to try to determine how much money he had on Sunday. This is Ted's spending pattern:
| Day | Debit ($) | Credit ($) |
| --------- | --------- | ---------- |
| Monday | 112 | --- |
| Tuesday | 141 | 18 |
| Wednesday | 56 | --- |
| Thursday | 28 | 70 |
| Friday | 22 | 42 |
| Saturday | 16 | 88 |
If the bank charges Ted an overdraft fee of $25 every time he overdraws his account, and Ted overdrew his account on Wednesday but not on Friday, which of the following is a possible amount of money that Ted could have had in his account last Sunday? Assume that the only debits and credits not listed are overdraft fees.
a. $300
b. $280
c. $240
d. $200
Please select the best answer from the choices provided
Answer (2)
Calculate total debits and credits to determine the balance range.
Establish the upper bound for Sunday's balance S based on the Wednesday overdraft: S < 291 .
Establish the lower bound for Sunday's balance S based on no overdraft on Friday: S ≥ 254 .
Identify the option within the range 254 ≤ S < 291 , which is 280 .
Explanation
Analyzing the Problem Let's analyze Ted's spending pattern to determine a possible amount of money he had last Sunday. We'll consider the debits, credits, and the overdraft fee to establish a range for his Sunday balance.
Defining the Variable Let S be the amount of money Ted had on Sunday. We need to find a possible value for S from the given options.
Calculating Total Debits (Mon-Wed) First, let's calculate the total debits from Monday to Wednesday. These are the debits that led to the overdraft on Wednesday. The total debit is 112 + 141 + 56 = 309 .
Determining the Upper Bound for S The total credit from Monday to Wednesday is 18 . Since Ted overdrew his account on Wednesday, his balance before the overdraft fee must have been negative. This means S + 18 − 309 < 0 , so S < 309 − 18 = 291 .
Accounting for the Overdraft Fee Ted was charged an overdraft fee of $25 on Wednesday. So, after the overdraft fee, his balance was S + 18 − 309 − 25 = S − 316 .
Analyzing Thursday and Friday Now, let's consider the period from Thursday to Friday. The total debits are 28 + 22 = 50 , and the total credits are 70 + 42 = 112 . Since Ted did not overdraw on Friday, his balance before Friday's transactions must have been non-negative.
Determining the Lower Bound for S The balance after Wednesday's overdraft fee is S − 316 . After Thursday and Friday's transactions, the balance is S − 316 + 70 + 42 − 28 − 22 = S − 316 + 112 − 50 = S − 254 . Since he did not overdraw on Friday, we have S − 254 ≥ 0 , which means S ≥ 254 .
Finding the Possible Value of S So, we have 254 ≤ S < 291 . Now we check which of the given options falls within this range: a. $300 , b. $280 , c. $240 , d. $200 . Only $280 falls within the range 254 ≤ S < 291 .
Final Answer Therefore, a possible amount of money that Ted could have had last Sunday is $280 .
Examples
Understanding spending patterns and avoiding overdraft fees is crucial for personal finance. For instance, if you're managing a budget and tracking expenses, knowing your minimum balance helps prevent unnecessary charges. This problem demonstrates how to analyze transactions and set financial goals to maintain a healthy financial standing. By carefully monitoring income and expenses, you can ensure you have enough funds to cover your obligations and avoid costly overdraft fees.
Ted could have had at least $254 and no more than $290 last Sunday based on his spending pattern. Among the answer choices given, $280 is the only option that fits within this range. Therefore, the best answer is option b: $280.
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