Final answer:
To calculate the total cost after a 25% discount and a 7% sales tax on a $3 item, you first find the amount of the discount and subtract it from the original price, then calculate the sales tax on the discounted price and add it to get the total. The provided options do not correctly represent this calculation, and there may be a typographical error in the question.
Step-by-step explanation:
The question asks to write an expression that represents the total amount Adam paid at the register after applying a 25% discount and then adding a 7% sales tax to a $3 item. To solve this, let's first calculate the discount by converting the percentage to a decimal and multiplying it by the item's cost:
$3 × 0.25 = $0.75
Subtract the discount from the original price to find the discounted price:
$3 - $0.75 = $2.25
Next, calculate the sales tax by converting the percentage to a decimal and multiplying it by the discounted price:
$2.25 × 0.07 = $0.1575
Now, add the sales tax to the discounted price to find the total amount paid:
$2.25 + $0.1575 ≈ $2.41
Since the question is asking for an expression in terms of x, and x is not defined in the context, it seems there might be a typographical error. Assuming the item's cost is represented by x, an expression representing the total amount paid would be:
0.75x + 0.07(x - 0.75x)
However, since x is given as $3, we can simply replace x with 3 and collapse the expression to match one of the provided options:
0.75× 3 + 0.07(3 - 0.75× 3)
This matches the process shown above, but none of the provided options are correct when considering the steps we've taken. Therefore, the expressions given in the options seem to be incorrectly constructed for the context of this problem.