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Sagot :
To determine why Adrienne's balance is incorrect, let's go through her transactions step-by-step and verify the calculations.
1. Initial Balance
Adrienne's beginning account balance was [tex]$320.00. 2. ATM Withdrawal and Fee Adrienne withdrew $[/tex]60.00 from the ATM, which incurred an additional [tex]$2.00 fee. The total amount debited for this transaction is: \[ 60.00 \text{ (withdrawal)} + 2.00 \text{ (fee)} = 62.00 \] Therefore, her balance after this transaction would be: \[ 320.00 - 62.00 = 258.00 \] 3. Grocery Store Transaction Adrienne then spent $[/tex]32.50 at the grocery store.
Her balance after the grocery transaction would be:
[tex]\[ 258.00 - 32.50 = 225.50 \][/tex]
4. Paycheck Deposit
Adrienne deposited her paycheck of [tex]$1,200.00. Her balance after the paycheck deposit would be: \[ 225.50 + 1,200.00 = 1,425.50 \] Based on these transactions, the correct final balance should be: \[ 1,425.50 \] However, the reported balance in the ledger is $[/tex]1,545.50.
Next, let's determine why there is a discrepancy:
- The reported balance is:
[tex]\[ 1,545.50 \][/tex]
- The correct balance should be:
[tex]\[ 1,425.50 \][/tex]
The difference between the reported balance and the correct balance is:
[tex]\[ 1,545.50 - 1,425.50 = 120.00 \][/tex]
This [tex]$120.00 difference indicates there is an error in Adrienne's ledger. Let's examine the potential mistakes: 1. Adrienne forgot to include the $[/tex]2.00 ATM transaction fee. This is not a factor here, because we included the ATM fee in our calculations and still have a discrepancy.
2. Adrienne deducted [tex]$23.50 from her balance instead of $[/tex]32.50.
Let's calculate what would have happened if Adrienne had only deducted [tex]$23.50 for the grocery transaction: - Correct grocery deduction: \[ 32.50 \] - Incorrect grocery deduction: \[ 23.50 \] - Difference: \[ 32.50 - 23.50 = 9.00 \] Even accounting for just this $[/tex]9.00 error in the grocery transaction isn't enough to explain the [tex]$120.00 discrepancy. Therefore, the $[/tex]120.00 discrepancy might be due to combined multiple errors. Focusing first on the major issues already identified, likely errors need revisiting the entries or perhaps an incorrect larger transaction deduction, which could include both noted potential errors.
The simplified key takeaway is an evident larger principle mistake:
1. The identified ATM and grocery deviations, coupled with further erroneous deductions.
Correcting for precise balance verification aided verification requires rechecking all transactional accuracy beyond these mentioned faulty considerations.
1. Initial Balance
Adrienne's beginning account balance was [tex]$320.00. 2. ATM Withdrawal and Fee Adrienne withdrew $[/tex]60.00 from the ATM, which incurred an additional [tex]$2.00 fee. The total amount debited for this transaction is: \[ 60.00 \text{ (withdrawal)} + 2.00 \text{ (fee)} = 62.00 \] Therefore, her balance after this transaction would be: \[ 320.00 - 62.00 = 258.00 \] 3. Grocery Store Transaction Adrienne then spent $[/tex]32.50 at the grocery store.
Her balance after the grocery transaction would be:
[tex]\[ 258.00 - 32.50 = 225.50 \][/tex]
4. Paycheck Deposit
Adrienne deposited her paycheck of [tex]$1,200.00. Her balance after the paycheck deposit would be: \[ 225.50 + 1,200.00 = 1,425.50 \] Based on these transactions, the correct final balance should be: \[ 1,425.50 \] However, the reported balance in the ledger is $[/tex]1,545.50.
Next, let's determine why there is a discrepancy:
- The reported balance is:
[tex]\[ 1,545.50 \][/tex]
- The correct balance should be:
[tex]\[ 1,425.50 \][/tex]
The difference between the reported balance and the correct balance is:
[tex]\[ 1,545.50 - 1,425.50 = 120.00 \][/tex]
This [tex]$120.00 difference indicates there is an error in Adrienne's ledger. Let's examine the potential mistakes: 1. Adrienne forgot to include the $[/tex]2.00 ATM transaction fee. This is not a factor here, because we included the ATM fee in our calculations and still have a discrepancy.
2. Adrienne deducted [tex]$23.50 from her balance instead of $[/tex]32.50.
Let's calculate what would have happened if Adrienne had only deducted [tex]$23.50 for the grocery transaction: - Correct grocery deduction: \[ 32.50 \] - Incorrect grocery deduction: \[ 23.50 \] - Difference: \[ 32.50 - 23.50 = 9.00 \] Even accounting for just this $[/tex]9.00 error in the grocery transaction isn't enough to explain the [tex]$120.00 discrepancy. Therefore, the $[/tex]120.00 discrepancy might be due to combined multiple errors. Focusing first on the major issues already identified, likely errors need revisiting the entries or perhaps an incorrect larger transaction deduction, which could include both noted potential errors.
The simplified key takeaway is an evident larger principle mistake:
1. The identified ATM and grocery deviations, coupled with further erroneous deductions.
Correcting for precise balance verification aided verification requires rechecking all transactional accuracy beyond these mentioned faulty considerations.
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