Let's walk through the steps methodically:
1. Known values:
- Beginning Balance: \$889.23
- Fence repair: \$75.86
- Dry cleaning: \$32.38
- Paycheck: \$140.91
- Gift from cousin: \$35.00
- Car payment: \$178.66
- Tax refund: \$66.18
- New chair: \$161.55
- Ending Balance recorded by Katie: \$682.87
- Ending Balance per bank statement: \$707.10
2. Calculating Total Credits:
- Credits include the Beginning Balance, Paycheck, Gift, and Tax Refund.
[tex]\[
\text{Total Credits} = 889.23 + 140.91 + 35.00 + 66.18 = 1131.32
\][/tex]
3. Calculating Total Debits:
- Debits include Fence repair, Dry cleaning, Car payment, and New chair.
[tex]\[
\text{Total Debits} = 75.86 + 32.38 + 178.66 + 161.55 = 448.45
\][/tex]
4. Calculating Expected Balance:
- The Expected Balance is the Total Credits minus the Total Debits.
[tex]\[
\text{Expected Balance} = 1131.32 - 448.45 = 682.87
\][/tex]
This ties in with Katie's recorded Ending Balance of \[tex]$682.87. But the bank statement says her balance is \$[/tex]707.10.
5. Calculating the Discrepancy:
- The discrepancy between the bank's balance and Katie's balance:
[tex]\[
\text{Discrepancy} = 707.10 - 682.87 = 24.23
\][/tex]
Now, let's evaluate each possible explanation:
### Option a: Neighbor paid for half of the fence repair.
- Half of the fence repair cost is:
[tex]\[
\frac{75.86}{2} = 37.93
\][/tex]
- Corrected Balance:
[tex]\[
682.87 + 37.93 = 720.80
\][/tex]
- This does not match the bank’s balance of \$707.10.
### Option b: Cost of dry cleaning should be \$23.38.
- Difference due to transposition:
[tex]\[
32.38 - 23.38 = 9.00
\][/tex]
- Corrected Balance:
[tex]\[
682.87 + 9.00 = 691.87
\][/tex]
- This does not match the bank’s balance of \$707.10.
### Option c: Chair was actually \$137.32 due to a 15% discount.
- Discount difference:
[tex]\[
161.55 - 137.32 = 24.23
\][/tex]
- Corrected Balance:
[tex]\[
682.87 + 24.23 = 707.10
\][/tex]
- This matches the bank’s balance.
### Option d: Tax refund was actually double.
- Double the received refund:
[tex]\[
66.18 \times 2 = 132.36
\][/tex]
- Difference from recorded:
[tex]\[
132.36 - 66.18 = 66.18
\][/tex]
- Corrected Balance:
[tex]\[
682.87 + 66.18 = 749.05
\][/tex]
- This does not match the bank’s balance.
### Conclusion:
The only explanation where the corrected balance matches the bank’s balance of \[tex]$707.10 is Option c. Katie's new chair was on sale for 15% off, making it cost \$[/tex]137.32, but she wrote down the before-sale price.
