Question

3. Suppose you pay $24 for a pair of shoes that has been discounted 20%. What is the original price of the shoes? Show how you identify what you are looking for, set up an equation, arrive at your answer, and check your work. Then clearly state your answer.

Answer 1

Discounted price = 24
discount rate = 20%

When an object is sold at a discount.
You can simply multiply the original price by the discount rate to get the value of the discount.

 Original Price * Discount Rate = Value of the discount

Then, you subtract the value of the discount from the Original price to get the discount price

Original Price - Value of the discount = discounted price

Remember: The discount price can also be arrived at by multiplying the Original price with the difference of 100% and the discount rate, in its decimal form.

Original price * (100%-discount rate)/100 = Discount Price

Using the latest formula, we can compute for the original price by dividing the discount price by the difference of 100% and the discount rate, in its decimal form.

Original Price = Discount Price / (100%-discount rate)/100

Original Price = 24 / (100%-20%)/100
                       = 24 / 0.80
Original Price = 30

Discount Value = 30 * 20%/100%
                          = 30 * 0.20
Discount Value = 6

Discount Price = 30 - 6
Discount Price = 24