If a shopkeeper sells an item for $120 after giving a discount of 20%, what was

If a shopkeeper sells an item for $120 after giving a discount of 20%, what was the original price?

If a shopkeeper sells an item for $120 after giving a discount of 20%, what was the original price?

Step 1: Understand that the shopkeeper sells an item for $120 after giving a discount of 20%.
Step 2: Let the original price of the item be represented by 'x'.
Step 3: Since a 20% discount is given, the selling price is 80% of the original price. This can be written as: Selling Price = Original Price - Discount.
Step 4: The discount can be calculated as 20% of 'x', which is 0.2x.
Step 5: Therefore, the selling price can be expressed as: 120 = x - 0.2x.
Step 6: Simplify the equation: 120 = 0.8x (because x - 0.2x = 0.8x).
Step 7: To find 'x', divide both sides of the equation by 0.8: x = 120 / 0.8.
Step 8: Calculate the value: x = 150.
Step 9: Conclude that the original price of the item was $150.

Percentage Calculation – Understanding how to calculate discounts and their impact on original prices.
Algebraic Manipulation – Using algebra to solve for the original price based on the discounted price.