Leather Wallet Pricing: A Business Math Puzzle
Let's dive into a fascinating scenario from the A. 28 de Julio artisan fair, where Susana, an enterprising entrepreneur, is selling her unique leather wallets. This problem combines elements of cost, profit margin, and discounts to challenge our understanding of pricing strategies. To solve this, we'll need to break down the information piece by piece and use algebraic equations to find our answer. So, grab your thinking caps, guys, and let's unravel this business math puzzle together!
Setting the Stage: Susana's Leather Wallet Business
Imagine the vibrant atmosphere of the artisan fair; the colorful stalls, the hum of conversation, and the array of handcrafted goods. Amidst this lively scene, Susana showcases her beautifully designed leather wallets, each adorned with intricate fabric appliques. She decides to price one of these wallets at S/150. This selling price is crucial, but what lies beneath it? To truly understand Susana's business strategy, we need to delve into the costs involved and the profit she aims to make.
Understanding Cost and Profit: In business, the cost of a product refers to the total expenses incurred in producing or acquiring it. This can include the cost of raw materials (like leather and fabric), labor costs (Susana's time and effort), and any other overhead expenses. Profit, on the other hand, is the difference between the selling price and the cost price. It represents the financial gain Susana makes from selling her wallets. In this scenario, Susana aims for a 25% profit margin on the cost of each wallet. This means she wants to earn 25% of the cost price as profit. Let's represent the cost price with the variable 'C'. Therefore, her profit would be 0.25 * C.
The Twist: Discount Dynamics: Here's where the puzzle gets interesting! Susana's profit isn't just a straightforward calculation. She mentions that the profit she earns is equal to the discount she applies to the original price. This introduces another layer of complexity. A discount is a reduction in the original selling price of a product. Retailers often use discounts to attract customers, clear out inventory, or stay competitive. The key here is that the amount of the discount is equal to the profit earned. If we let 'D' represent the discount amount, then D = 0.25 * C. This equality forms the foundation of our problem-solving approach.
Formulating the Equation: Now we can formulate a clear equation. The selling price (S/150) is equal to the original price minus the discount. But what was the original price? This is what we need to find out. We know that the selling price is also equal to the cost price plus the profit. Putting it all together, we have:
Original Price - Discount = Selling Price Cost Price + Profit = Selling Price
Since Discount = Profit, we can infer that the Original Price is higher than the Cost Price. The difference between them is twice the Profit (or twice the Discount). Let's use 'P' to represent the original price of the wallet. Our equation becomes:
P - D = 150
And we also know that D = 0.25 * C. Therefore:
P - (0.25 * C) = 150
We also know that the selling price is the cost plus a 25% profit:
C + (0.25 * C) = 150
This simplifies to:
1.25 * C = 150
Now we can solve for C and then use that value to find P.
Unraveling the Solution: Step-by-Step Calculation
Alright, guys, let's put on our math hats and crunch these numbers! We've established that Susana's selling price (S/150) represents the cost price plus a 25% profit margin. This crucial piece of information allows us to calculate the cost price. Once we know the cost price, we can then determine the original price of the wallet.
Calculating the Cost Price (C): As we derived earlier, the equation representing the selling price in relation to the cost price is:
- 25 * C = 150
To isolate 'C' and find the cost price, we simply divide both sides of the equation by 1.25:
C = 150 / 1.25
C = 120
Therefore, the cost price of the leather wallet is S/120. This means Susana spends S/120 to produce or acquire each wallet before adding her profit margin.
Determining the Discount (D): Remember, the problem stated that Susana's profit is equal to the discount she offers. We know that her profit is 25% of the cost price. Now that we know the cost price, we can easily calculate the discount:
D = 0. 25 * C
D = 0.25 * 120
D = 30
So, the discount Susana applies to the original price of the wallet is S/30. This discount plays a key role in attracting customers and influencing their purchasing decisions.
Calculating the Original Price (P): Now that we know the selling price (S/150) and the discount (S/30), we can easily calculate the original price of the wallet. We know that:
Original Price - Discount = Selling Price
Therefore:
P - 30 = 150
To find 'P', we add 30 to both sides of the equation:
P = 150 + 30
P = 180
Therefore, the original price of the leather wallet was S/180. This is the price Susana initially intended to sell the wallet for before applying the discount.
Final Answer: The Original Price of the Wallet
After meticulously analyzing the information provided and applying our algebraic skills, we've arrived at the solution. The original price of the leather wallet, before any discounts were applied, was S/180. This means that Susana initially planned to sell the wallet for S/180, but she offered a discount of S/30, bringing the final selling price down to S/150.
In Conclusion: This problem illustrates the interconnectedness of cost, profit, and discounts in a business setting. By understanding these relationships, entrepreneurs like Susana can make informed decisions about pricing their products to maximize profits while remaining competitive in the market. And for us, it's a fun exercise in applying math to real-world scenarios! Good job, guys!