The Profitable Watermelon Seller: A Mathematical Mystery Solved

Introduction to the Problem

In the dynamic world of retail, understanding the revenue and profit margins is crucial for success. A simple situation in the retail fruit business can often times present an intriguing problem to solve. For example, let's consider a fruit seller who bought some watermelons and had to deal with an unexpected twist. Here's how we can unravel the mystery.

The Watermelon Seller's Challenge

The seller went to the market and bought a certain number of watermelons at a price of GHS 5.00 each.

Unfortunately, 12 of the watermelons turned out to be rotten, reducing the quantity that could be sold.

After selling the remaining watermelons at GHS 7.00 each, the seller made a profit of GHS 150.00.

Solving the Mathematical Problem

Let's denote the number of watermelons the fruit seller bought as ( x ).

Step 1: Total Cost

The cost price per watermelon is GHS 5.00. Therefore, the total cost price for ( x ) watermelons is:

[ text{Total Cost} 5x ]

Step 2: Number of Good Watermelons Sold

The seller realized that 12 watermelons were rotten, so the number of good watermelons sold is:

[ text{Good Watermelons} x - 12 ]

Step 3: Total Revenue

The selling price per good watermelon is GHS 7.00. Therefore, the total revenue for the good watermelons is:

[ text{Total Revenue} 7(x - 12) ]

Step 4: Profit Calculation

The profit made by the seller is given as GHS 150.00. We can express profit as:

[ text{Profit} text{Total Revenue} - text{Total Cost} ]

Substituting the expressions we have:

[ 150 7(x - 12) - 5x ]

Step 5: Simplifying the Equation

Let's simplify the equation step by step:

[ 150 7x - 84 - 5x ] [ 150 2x - 84 ] [ 150 84 2x ] [ 234 2x ] [ x frac{234}{2} 117 ]

Conclusion

Thus, the fruit seller bought 117 watermelons.

This problem brilliantly illustrates the importance of mathematical proficiency in retail and financial management in the retail fruit business. Such skills are not only useful for solving problems faced by sellers but also for making informed decisions that enhance business profitability.