Question

The sale price of an item is $65. This sale price reflects a discount of 15% off the item's retail price. Find the retail price r in dollars.

Answer 1

To calculate the retail price r of an item that is on sale for $65 after a 15% discount, we identify that $65 represents 85% of the original price. By setting up the equation $65 = r x 0.85 and solving for r, we find that the retail price r is approximately $76.47.

Step-by-step explanation:

To find the retail price r before the discount, we can use the sale price information given and the percent discount to work backwards. The item on sale is $65 after a 15% discount. This means $65 is 85% (100% - 15%) of the original price.

Let's set up the equation using the percent in decimal form:

1. Convert the percentage to a decimal by dividing by 100, which gives us 0.85.
2. Set up the equation: Sale Price = Retail Price (1 - Discount Rate).
3. Plug in the values: $65 = r × 0.85.
4. Solve for r (retail price) by dividing both sides of the equation by 0.85.
5. The calculation will be $65 / 0.85 = $76.47.
6. The retail price r is approximately $76.47 before the discount.