Final answer:
The amount charged on Kate's mom's credit card will be $178.62.
Step-by-step explanation:
To calculate the amount charged on Kate's mom's credit card, we'll first apply the AIR Trans discount of 33% to the ticket price. This is calculated by multiplying the ticket price ($248) by 0.33, which gives us a discount of $81.84. Subtracting the discount from the ticket price, we find that Kate will be charged $166.16 for the airline ticket.
Next, we'll calculate the sales tax. Given that the sales tax rate in Charlotte is 7.5%, we can find the tax amount by multiplying the ticket price after the discount ($166.16) by 0.075. The sales tax comes out to be $12.46.
Finally, we add the ticket price after the discount ($166.16) and the sales tax ($12.46) to get the total amount charged on Kate's mom's credit card, which is $178.62.