Sunglasses Math: Cost, Profit, And Percentage Explained

Hey guys! Let's dive into a cool math problem about Tiro and his sunglasses business. We're going to break down the costs, sales, and profits to really understand what's going on. It's like being a financial detective, but with cooler accessories (sunglasses, obviously!). We'll tackle the cost of each pair, the total profit, and even calculate the percentage profit. So, grab your mental calculators, and let's get started!

a) What is the Cost Price of One Pair of Sunglasses?

To figure out the cost price of just one pair of sunglasses, we need to divide the total cost Tiro paid for all the sunglasses by the number of pairs he bought. Think of it like splitting a bill among friends. Tiro spent P 112 on 20 pairs. So, the cost price per pair is P 112 divided by 20.

Let's do the math: P 112 / 20 = P 5.60

So, each pair of sunglasses cost Tiro P 5.60. This is a crucial piece of information because it tells us how much Tiro initially invested in each pair. This cost price becomes our baseline for calculating profit later on. Imagine you're buying ingredients for a cake; the cost of those ingredients is like the cost price of the sunglasses – it's what you spent to get started. Knowing the cost price is essential for any business because it helps you determine how much to sell your product for to make a profit.

Now, let's break this down a bit further. Why is it important to know the individual cost price? Well, if Tiro didn't know this, he wouldn't be able to accurately assess his profits. He might think he's making more money than he actually is, or he might underprice his sunglasses and lose potential earnings. In a real-world scenario, businesses use cost price calculations to make informed decisions about pricing, discounts, and overall financial strategy. For example, if Tiro knew his cost price was P 5.60, he could decide to sell each pair for P 10, as he did, and confidently calculate his profit margin. If the cost price was higher, say P 8, he might need to adjust his selling price to ensure he still makes a reasonable profit. Understanding the cost price is also vital for inventory management. Tiro needs to know how much money is tied up in his sunglasses inventory so he can make smart purchasing decisions in the future.

In summary, finding the cost price of one item when you know the total cost and the quantity is a fundamental concept in business and everyday life. It's a simple division problem, but it unlocks a wealth of information that can help you make smarter financial choices. So, whether you're buying sunglasses, ingredients, or anything else, remember to calculate the cost price per item – it's a key to financial savvy!

b) How Much Profit Does Tiro Make If He Sells All 20 Pairs of Sunglasses?

Alright, let's calculate Tiro's profit! To figure this out, we need to know how much money he made in total and then subtract how much he spent. Profit is essentially the difference between revenue (money coming in) and cost (money going out).

Tiro sold each pair of sunglasses for P 10, and he sold all 20 pairs. So, his total revenue is 20 pairs multiplied by P 10 per pair. Let's calculate that: 20 * P 10 = P 200

So, Tiro made P 200 from selling all the sunglasses. Now, we need to subtract his total cost, which we know is P 112. Profit is calculated as Total Revenue - Total Cost. So, P 200 - P 112 gives us Tiro's profit.

P 200 - P 112 = P 88

Therefore, Tiro made a profit of P 88 from selling all 20 pairs of sunglasses. This is a pretty good outcome! It means that after covering his initial investment, Tiro has an extra P 88 in his pocket. Understanding profit is absolutely crucial in any business venture. It's the indicator of success and sustainability. If Tiro's profit was negative, that would mean he lost money on the deal, which is definitely not what you want!

Let's think about why understanding profit is so important. Profit isn't just about having extra money; it's about the ability to reinvest in your business, grow your operations, and even take home a salary. If Tiro wanted to buy more sunglasses to sell, he could use some of his profit to do that. If he wanted to expand his business and maybe sell other accessories, his profit would help him fund that expansion. Profit also provides a cushion for unexpected expenses or slow sales periods. It's a financial safety net that can help a business weather tough times.

Furthermore, calculating profit helps Tiro assess the viability of his business model. If his profit margin (the percentage of revenue that is profit) is too low, he might need to adjust his pricing strategy, find cheaper suppliers, or reduce his operating costs. A healthy profit margin indicates that the business is efficient and sustainable in the long run. For example, if Tiro had spent P 180 on the sunglasses and sold them for P 200, his profit would only be P 20. This would be a much lower profit margin, and Tiro might need to rethink his approach.

In conclusion, calculating total profit is a fundamental step in evaluating the success of a business transaction. It's a simple calculation, but it provides valuable insights into the financial health of the venture. Tiro's profit of P 88 tells us that his sunglasses business is off to a good start, and with smart management, he can continue to grow his earnings.

c) Calculate the Percentage Profit

Now, let's take our analysis a step further and calculate Tiro's percentage profit. The percentage profit gives us a relative measure of how profitable Tiro's venture was. It tells us what percentage of his cost price he earned as profit. This is a really useful metric for comparing the profitability of different ventures or for tracking the performance of a business over time.

The formula for percentage profit is: (Profit / Cost Price) * 100

We already know Tiro's profit (P 88) and his total cost price (P 112). So, let's plug those values into the formula:

(P 88 / P 112) * 100

First, we divide the profit by the cost price: P 88 / P 112 = 0.7857 (approximately)

Then, we multiply that result by 100 to express it as a percentage: 0.7857 * 100 = 78.57%

So, Tiro's percentage profit is approximately 78.57%. This means that for every P 1 Tiro invested, he earned about P 0.79 in profit. That's a pretty impressive return! A high percentage profit indicates that Tiro is running a very efficient and profitable business.

Let's delve deeper into why percentage profit is such a valuable metric. While the total profit (P 88) tells us how much money Tiro made in absolute terms, the percentage profit (78.57%) gives us a sense of how efficient his investment was. For example, if Tiro had invested P 500 in a different venture and made a profit of P 100, his total profit would be higher than in the sunglasses case. However, his percentage profit would be much lower: (P 100 / P 500) * 100 = 20%. This shows that the sunglasses venture was actually more profitable relative to the investment made.

Percentage profit is also a crucial tool for comparing the performance of different businesses or investments. If Tiro was considering investing in another product line, he could calculate the percentage profit for each line and choose the one that offers the highest return on investment. This helps him make informed decisions about where to allocate his resources.

Moreover, tracking percentage profit over time can help Tiro identify trends and potential problems in his business. If his percentage profit is declining, it might indicate that his costs are rising, his sales are falling, or his pricing strategy needs to be adjusted. By monitoring this metric, Tiro can take proactive steps to maintain or improve his profitability.

In summary, calculating the percentage profit provides a valuable perspective on the profitability of a business venture. It allows for comparisons, helps in decision-making, and provides insights into the efficiency of the investment. Tiro's impressive percentage profit of 78.57% highlights the success of his sunglasses business and provides a solid foundation for future growth.

So, there you have it! We've successfully dissected Tiro's sunglasses deal, calculated his cost price, total profit, and percentage profit. Hopefully, this has given you a better understanding of these key financial concepts. Keep these principles in mind, and you'll be a financial whiz in no time!