Calculate The Cost Of Nine Bags

When you encounter problems that ask you to find the cost of a different quantity of items based on a given price for a certain number of items, it's a classic case of proportional reasoning. The core idea is to first determine the cost of a single item and then use that information to calculate the cost of the desired number of items. This method is fundamental in mathematics and has practical applications in everyday life, from grocery shopping to budgeting. Let's dive into how we can solve this specific problem: Seven bags cost ₹59.50. How much do nine bags cost? The initial step involves finding the price of one bag. To do this, we divide the total cost of the seven bags by the number of bags, which is seven. So, ₹59.50 divided by 7 gives us the cost per bag. This calculation is crucial because it establishes the unit price, the foundation upon which all further calculations will be based. Understanding the unit price allows us to scale the cost up or down proportionally. It's like finding the 'building block' cost before you can construct the final price for a larger quantity. This process is not just for this specific problem; it's a universal mathematical concept that helps demystify how pricing works in many scenarios. Whether you're comparing deals at the supermarket or trying to figure out the value of bulk purchases, the principle of finding the unit price remains the same. It empowers you with the knowledge to make informed decisions and avoid overpaying. So, let's get our calculators ready or prepare for some simple division to uncover the cost of a single bag!

Finding the Unit Price: The First Crucial Step

To accurately determine how much nine bags cost, we must first establish the price of a single bag. This is often referred to as the 'unit price.' In our problem, we know that seven bags together cost ₹59.50. To find the cost of just one bag, we perform a simple division: the total cost divided by the number of items. Therefore, we will divide ₹59.50 by 7. This calculation is the bedrock of solving this type of problem. It allows us to break down a bulk price into its most basic component. Think of it like this: if a baker sells a dozen cookies for $12, you first figure out that each cookie costs $1 ($12 / 12 cookies). Once you have that unit price, you can then figure out how much, say, 20 cookies would cost ($1 * 20 = $20). This methodical approach ensures accuracy and makes the subsequent steps straightforward. The result of ₹59.50 divided by 7 will give us the exact price for one bag. It’s important to be precise in this calculation, as any error here will propagate through to the final answer. For instance, if the division results in a repeating decimal, we might need to round it to two decimal places (for currency) or keep it as a fraction for maximum accuracy until the final step, depending on the context and instructions. This stage is all about precision and understanding the value of each individual item within the larger group. Mastering this step is key to confidently solving any problem involving proportional costs. It's a skill that extends far beyond textbooks and into the realm of smart consumerism and financial planning.

Performing the Division: Uncovering the Cost Per Bag

Now, let's get down to the actual calculation. We need to divide ₹59.50 by 7. This is the core mathematical operation that will reveal the cost of a single bag. Performing this division, we find that ₹59.50 ÷ 7 = ₹8.50. So, each bag costs ₹8.50. This is our unit price. It's a crucial piece of information that we'll use in the next step. Double-checking this division is always a good practice. You can do this by multiplying the unit price back by the number of bags: ₹8.50 * 7 = ₹59.50. This confirms our calculation is correct. This process of finding the unit price is fundamental to many mathematical problems, especially those involving ratios and proportions. It simplifies complex pricing scenarios into understandable steps. For example, if you see a 'buy 2 get 1 free' offer, you can use the unit price to determine if it's truly a good deal. You'd calculate the effective price per item in the offer and compare it to the standard unit price. In our case, knowing that one bag costs ₹8.50 makes it easy to figure out the cost of any number of bags. This systematic approach ensures that we are building our solution on a solid foundation of accurate calculations. It's not just about getting the right answer; it's about understanding how we got there, which builds mathematical confidence and competence. This is the point where the problem starts to become much clearer, as we now have a definitive value for each individual item.

Calculating the Cost of Nine Bags

With the unit price of a single bag firmly established at ₹8.50, we can now confidently calculate the cost of nine bags. This is the final step in our problem-solving process. To find the total cost for nine bags, we simply multiply the cost of one bag by the desired number of bags. That is, we multiply ₹8.50 by 9. This is where the utility of finding the unit price becomes crystal clear. It allows us to easily scale up the cost for any quantity. The calculation is as follows: ₹8.50 * 9. Performing this multiplication will give us the final answer. This step is straightforward once the unit price is known. It's a direct application of multiplication, reinforcing the concept of proportional relationships. Many real-world scenarios involve this kind of scaling. For instance, if you're planning a party and need to buy enough juice boxes for 50 guests, and you know the price of a 6-pack, you'd first find the price per juice box and then multiply by 50. This illustrates the practical power of understanding unit prices. The multiplication of ₹8.50 by 9 is the culmination of our efforts. It brings together all the information and calculations to provide the definitive cost for nine bags. This is the moment of truth, where we see the final figure emerge from our systematic approach. It’s a satisfying conclusion to a problem that might initially seem complex but is, in reality, quite manageable with the right steps.

The Final Calculation and Answer

Let's complete the final calculation: ₹8.50 multiplied by 9. This multiplication yields ₹76.50. Therefore, nine bags cost ₹76.50. This is the solution to our problem. We've successfully navigated the steps of finding the unit price and then scaling it up to the required quantity. This method is robust and can be applied to any similar problem where you need to determine the cost of a different number of items based on a given quantity and price. It’s a testament to the power of proportional reasoning in mathematics. To verify our answer, we can think about the relationship: 7 bags cost ₹59.50, and 9 bags cost ₹76.50. Since 9 bags is more than 7 bags, the cost should be higher, which it is. The increase in cost should be proportional to the increase in the number of bags. The difference in bags is 9 - 7 = 2 bags. The cost of these 2 extra bags would be 2 * ₹8.50 = ₹17.00. And indeed, ₹59.50 (cost of 7 bags) + ₹17.00 (cost of 2 extra bags) = ₹76.50, which is our calculated cost for 9 bags. This self-checking mechanism is an excellent way to build confidence in your mathematical solutions. It demonstrates that the answer is consistent and logically derived. This problem, while simple, highlights a fundamental mathematical concept that is incredibly useful. The ability to break down problems, find unit values, and then re-scale them is a skill that serves you well in many aspects of life, from personal finance to more complex scientific and engineering applications. It's about making sense of quantities and their associated values in a structured and logical manner. This structured approach to problem-solving is what makes mathematics such a powerful tool.

Conclusion: Mastering Proportional Costs

In summary, solving the problem of how much nine bags cost when seven bags cost ₹59.50 involves a straightforward two-step process. First, we found the unit price by dividing the total cost (₹59.50) by the number of bags (7), which gave us ₹8.50 per bag. Second, we calculated the cost for nine bags by multiplying this unit price (₹8.50) by nine, resulting in a total cost of ₹76.50. This method of using unit prices is a cornerstone of proportional reasoning and is incredibly versatile. It applies to countless real-world scenarios, from comparing prices at the grocery store to calculating material needs for a project. Understanding how to find and use unit prices empowers you to make informed decisions, save money, and manage your resources more effectively. It's a practical mathematical skill that transcends the classroom and is applicable to everyday life. The ability to break down complex pricing into manageable unit costs and then scale them up or down is a valuable asset. Always remember to check your work by verifying the relationships and ensuring your answer makes logical sense in the context of the problem. For further exploration into the world of ratios, proportions, and problem-solving techniques, you might find resources on www.khanacademy.org or www.mathsisfun.com to be incredibly helpful. These platforms offer a wealth of information, examples, and practice problems to hone your mathematical skills.