Calculating the Original Price of a Book After a Discount
When dealing with discounts, it’s common to need to find the original price given the final price and the discount percentage. In this article, we will delve into a detailed explanation of how to calculate the original price of a book after it has been discounted. We will use two different methods to solve this problem, ensuring that you can understand and apply the math effectively.
Method One: Algebraic Approach
Let's assume the original price of a book to be X PHP (Philippine Peso). The book is sold at a discount of 33.5%, meaning it is sold at 66.5% (100% - 33.5%) of its original price. This can be expressed as:
66.5%
66.5% of the original price is equal to the final price.
Mathematically, this is expressed as:
0.665X 230
To solve for X, we rearrange the equation:
X 230 / 0.665
X 346.79, which we can round to 347 PHP (to the nearest whole number).
Let's verify the solution:
347 PHP * 33.5% 347 * 0.335 116.395 PHP disc
347 PHP - 116.395 PHP 230.605 PHP ≈ 230 PHP
The slight variation is due to rounding.
Method Two: Direct Calculation
The second method can be more straightforward. If the final price after a 33.5% discount is 230 pesos, we can work backwards to find the original price using the following steps:
Let’s assume the final price (230 PHP) is 66.5% of the original price (100% - 33.5%). We can express this as:
66.5% 230
1% 230 / 66.5 ≈ 3.46 PHP
100% (original price) 3.46 PHP * 100 ≈ 346 PHP
Thus, the original price of the book is 346 PHP.
Verifying the solution:
346 PHP * 33.5% 346 * 0.335 116.39 PHP disc
346 PHP - 116.39 PHP 230 PHP
This confirms that the original price is indeed 346 PHP.
Conclusion
Both methods yield the same result. The original price of the book, after a 33.5% discount, is 346 PHP (or approx. 347 PHP to the nearest whole number).
Additional Notes
If you were to round 33.5% to 33.333333333333333... (i.e., 33 1/3%), the calculation would be different due to the exact nature of the discount factor. In such a case, 230 pesos would represent 2/3 of the original price, leading to an original price of 345 PHP (since 2/3 of 345 is exactly 230).
Understanding these methods can be very useful in various scenarios, such as competitive exams, real-world business transactions, or personal finance management.