A store is offering a 20 percent discount on all items. The price of the hat after the discount is 18 dollars what was the original price
The Correct Answer and Explanation is:
To find the original price of the hat before the discount, we can use the formula for calculating the discounted price:Discounted Price=Original Price×(1−Discount Percentage)\text{Discounted Price} = \text{Original Price} \times (1 – \text{Discount Percentage})Discounted Price=Original Price×(1−Discount Percentage)
In this case:
- The discounted price is $18.
- The discount percentage is 20%, or 0.20 in decimal form.
So the formula becomes:18=Original Price×(1−0.20)18 = \text{Original Price} \times (1 – 0.20)18=Original Price×(1−0.20)18=Original Price×0.8018 = \text{Original Price} \times 0.8018=Original Price×0.80
To isolate the original price, divide both sides of the equation by 0.80:Original Price=180.80\text{Original Price} = \frac{18}{0.80}Original Price=0.8018Original Price=22.50\text{Original Price} = 22.50Original Price=22.50
Therefore, the original price of the hat was $22.50 before the discount.
Explanation:
When the store applies a 20% discount, you only pay 80% of the original price. To find the original price, we divide the price after the discount ($18) by the remaining percentage (0.80). The result gives us the original price, which in this case is $22.50.
This process is essentially reversing the discount calculation to figure out what the price was before the discount was applied.
