Final answer:
The correct formula for the final cost of an item after a 35% discount and 7% sales tax is applied is 0.65x + 0.0455x, where x is the original cost. Option B is the closest, but it incorrectly suggests that the sales tax applies to the original price.
Step-by-step explanation:
The question concerns calculating the final cost of an item after a promotional sale and sales tax are applied. The original cost of the item is represented by x. A 35% discount reduces the original price to 65% of its value, thus the cost after the discount is 0.65x. After applying the discount, a 7% sales tax is added to the reduced price.
To find the final cost, you first multiply the discounted price by the sales tax rate to calculate the tax amount, then add this tax to the discounted price. Therefore, the correct representation involving the original cost x is 0.65x (the price after the discount) plus 0.07 times 0.65x (the sales tax on the discounted price), which simplifies to 0.65x + 0.0455x.
Option B is the closest to the correct formula, but it does not account for the fact that the sales tax is applied only after the discount has been taken.