Finding Original Price from Sale Price

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Finding the original price of a discounted item is a practical skill that can help you understand how much you're saving during a sale. Here's a step-by-step guide:

Step 1: Understanding the Terms

Sale Price: This is the discounted price you pay for the item.
Discount: This is the percentage that the original price has been reduced by.
Original Price: This is the price of the item before the discount.

Step 2: Converting the Discount to Decimal Form

The discount percentage needs to be converted to a decimal to use in the formula. Divide the discount percentage by 100. For example, a 20% discount is $0.20$ in decimal form.

Step 3: Finding the Amount Discounted

The amount discounted from the original price is the sale price divided by $1 -$ the discount in decimal form.

Step 4: Calculate the Original Price

The original price is the sale price divided by $1 -$ the discount in decimal form. For example, if an item is on sale for $80 with a 20% discount, the original price is $80 divided by $1 - 0.20 = 0.80$. So, the original price is $100.

Step 5: Practice

Practice this skill with different examples to ensure you understand the process.

Example

Let's say you bought a shirt on sale for $40. The shirt was advertised as being 20% off the original price. You want to find out what the original price was.

Here's how you can calculate that:

Convert the discount to decimal form. A 20% discount becomes $0.20$.
Subtract the discount from 1. This would be $1 - 0.20 = 0.80$.
Finally, divide the sale price by your answer from step 2 to find the original price. In this case, it would be $$40 \div 0.80 = $50$.

So, the original price of the shirt was $50.

Exercises

1) If a book is on sale for $$45$ after a $10%$ discount, what was its original price?

2) A pair of shoes is sold for $$60$ after a $25%$ discount. What was the original price of the shoes?

3) A TV set was sold at $$540$ after a discount of $10%$. Find the original price of the TV set.

4) A dress is on sale for $$80$ after a $20%$ discount. What is the original price of the dress?

5) If you bought a bicycle for $$200$ after a discount of $20%$, what was the original price?

6) A jacket was purchased for $$90$ after a $30%$ discount. Find the original price of the jacket.

7) A laptop is sold for $$720$ after a $10%$ discount. What was the original price of the laptop?

8) A table is sold for $$180$ after a $40%$ discount. What is the original price of the table?

9) A watch was purchased for $$120$ after a discount of $20%$. Find the original price of the watch.

10) A game console is sold for $$300$ after a $25%$ discount. What was the original price of the game console?

Answers

1) The original price of the book was $$\frac{45}{0.9} = $50$

2) The original price of the shoes was $$\frac{60}{0.75} = $80$

3) The original price of the TV set was $$\frac{540}{0.9} = $600$

4) The original price of the dress was $$\frac{80}{0.8} = $100$

5) The original price of the bicycle was $$\frac{200}{0.8} = $250$

6) The original price of the jacket was $$\frac{90}{0.7} = $128.57$

7) The original price of the laptop was $$\frac{720}{0.9} = $800$

8) The original price of the table was $$\frac{180}{0.6} = $300$

9) The original price of the watch was $$\frac{120}{0.8} = $150$

10) The original price of the game console was $$\frac{300}{0.75} = $400$

Finding Original Price from Sale Price