A store offers a 4% discount if a consumer pays cash rather than paying by credit card. If the cash price of an item is $84.00, what is the credit card purchase price of the same item?

Answer

To find the credit card purchase price of an item that has a cash price of $84.00 with a 4% discount, we can follow these steps:

### Step 1: Understand the relationship between the cash price and the original price.
The cash price ($84.00) is the price after applying a 4% discount to the original price (let's denote it as X). Therefore, we can express this relationship mathematically as:
\[ \text{Cash Price} = \text{Original Price} \times (1 - \text{Discount Rate}) \]
In this case, the discount rate is 4%, or 0.04 in decimal form.

### Step 2: Set up the equation.
Using the relationship established in Step 1:
\[ 84 = X \times (1 - 0.04) \]
This simplifies to:
\[ 84 = X \times 0.96 \]

### Step 3: Solve for the original price (X).
To find X, we can rearrange the equation:
\[ X = \frac{84}{0.96} \]

### Step 4: Calculate the value of X.
Now, we perform the division:
\[ X = \frac{84}{0.96} \approx 87.5 \]

### Conclusion:
The credit card purchase price of the item is approximately $87.50.

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