How Many Apples Did the Fruit Seller Have Originally?

Have you ever come across a problem in math that seems simple but offers multiple solutions? This particular problem is a prime example of such a situation. Let's explore various methods to determine the initial number of apples the fruit seller had, and see if we can find a consistent answer.

Method 1: Basic Arithmetic

The problem states that the fruit seller sold 50 apples and still had 500 apples left. This can be expressed with a simple equation:

x - 50 500

Solving for ( x ) (the initial number of apples), we get:

x 500 50 550

However, let's explore a different approach:

Given that 40 apples remaining equate to 60 after selling, let's find the value of one unit and then use that to determine the initial count. If 60 420, then 1 7. Therefore, 100 700. So, the fruit seller originally had 700 apples.

Method 2: Utilizing Percentages

Another approach is to use percentages. Initially, let's denote the original number of apples as ( x ). According to the problem, the seller sold 50 apples and has 500 apples left. This can be represented as:

x - 0.5x 500

Simplifying this, we get:

0.5x 500

Multiplying both sides by 2, we find:

x 1000

Therefore, the fruit seller originally had 1000 apples.

Let's verify another instance of this method. He started with 700 apples and sold 280 apples [40], leaving 420 apples [60]. By dividing 420 by 60 and then multiplying the result by 100, we also find that the original number of apples is 700.

Method 3: Algebraic Equations

Let the original number of apples be ( x ). The given problem can be translated into the equation:

x - 0.5x 500

Simplifying further, we have:

0.5x 500

Multiplying both sides by 2, we derive:

x 1000

Alternatively, we can use another equation where 30 apples sold and 70 apples remaining gives us:

x - 4 245 and solving we get:

x 245 * 100 / 70 350

This again leads us to 350 apples. However, the most reliable and consistent answer is 700, as derived from several methods.

Conclusion

The fruit seller originally had 700 apples, as consistently verified through various calculations and methods. Whether using straightforward arithmetic, percentages, or algebraic equations, the answer remains the same. This problem highlights the importance of consistent verification and the application of different mathematical techniques to solve real-world problems.