Short Answer 
The total cost of the Chang’s family’s purchases before tax is $329.94. After calculating the sales tax at 6 3/5%, which amounts to $21.78, the final total amount paid is $351.72.
Step 1: Calculate the Total Cost of Purchases
First, gather all the prices of the items purchased by the Chang’s family. In this case, they bought:
- New Lamp: $89.95
- Comforter: $239.99
Add these amounts together to find the total cost without tax:
Total = $89.95 + $239.99 = $329.94
Step 2: Calculate the Sales Tax
Next, determine the sales tax that applies to the total cost. The sales tax rate is given as 6 3/5%, which converts to 0.066 in decimal form. Now, calculate the sales tax:
Sales Tax = Total Cost x Sales Tax Rate
Sales Tax = $329.94 x 0.066 = $21.78
Step 3: Find the Total Amount Paid
Finally, add the calculated sales tax to the original total cost to find the total amount the Chang’s family paid:
Total Amount Paid = Total Cost + Sales Tax
Total Amount Paid = $329.94 + $21.78 = $351.72
Thus, the Chang’s family paid the correct amount for their purchases, confirming that the answer is option D.