Final answer:
The credit-card purchase price of the item is $87.50.
Step-by-step explanation:
To find the credit-card purchase price, we need to calculate the original price before the 4% discount. Let's call the original price x.
Since the cash price is $84.00, the cash price is equal to 96% (100% - 4%) of the original price:
x * 0.96 = $84.00
To solve for x, we divide both sides of the equation by 0.96:
x = $84.00 / 0.96 = $87.50
Therefore, the credit-card purchase price of the same item is $87.50.