Exercise 5.3
1. The cost of a pair of shoes increases by $20 \%$ to E420.
(a) What percentage of the old price is the new price?
(b) Calculate the original price.
Answer (2)
The new price of E420 represents 120% of the original price. The original price of the shoes was E350 after solving the equation. Therefore, the original price before the 20% increase was E350.
;
The new price is 120% of the original price.
Set up the equation 1.20 x = 420 , where x is the original price.
Solve for x by dividing both sides by 1.20: x = 1.20 420 = 350 .
The original price is 350 .
Explanation
Understanding the Problem The problem states that the cost of a pair of shoes increased by 20% to $420. We need to find two things: (a) what percentage of the original price is the new price, and (b) the original price of the shoes.
Finding the Percentage (a) Since the price increased by 20%, the new price is the original price plus 20% of the original price. This means the new price is 100% (original price) + 20% (increase) = 120% of the original price.
Calculating the Original Price (b) Let the original price be x . The new price is the original price plus 20% of the original price, which can be written as: x + 0.20 x = 1.20 x We are given that the new price is $420. So, we have the equation: 1.20 x = 420 To find the original price x , we divide both sides of the equation by 1.20: x = 1.20 420 x = 350 Therefore, the original price of the shoes was $350.
Final Answer (a) The new price is 120% of the old price. (b) The original price of the shoes was $350.
Examples
Understanding percentage increases and calculating original prices is useful in many real-life situations. For example, when a store announces a sale with a certain percentage discount, you can calculate the original price of an item. Similarly, if you know the price of an item after tax and the tax percentage, you can calculate the price before tax. These skills are helpful for budgeting, shopping, and making informed financial decisions.
