Calculating The Cost Of One Pound Of Potatoes A Unit Price Problem

At its core, this mathematical problem involves calculating the unit price of potatoes given the total cost and weight of a sack. We are tasked with determining the cost of one pound of potatoes when a 10-pound sack is priced at $6.55. The solution requires a simple division operation, and the final answer must be rounded to the nearest cent. This exercise is a practical application of basic arithmetic, commonly encountered in everyday shopping and budgeting scenarios.

Breaking Down the Problem

To solve this problem effectively, we must focus on the fundamentals of unit price calculation. We know the total cost ($6.55) and the total weight (10 pounds). Our objective is to find the cost per pound. This involves dividing the total cost by the total weight. By doing so, we isolate the price of a single pound of potatoes, providing us with a clear understanding of the value we are getting for our money. This concept is not only useful in grocery shopping but also in various financial and economic analyses where understanding unit costs is crucial.

Calculation Steps

1. Identify the known values: The total cost of the sack of potatoes is $6.55, and the total weight is 10 pounds.
2. Set up the division: To find the cost per pound, we divide the total cost by the total weight: $6.55 ÷ 10.
3. Perform the division: $6.55 ÷ 10 = $0.655.
4. Round to the nearest cent: Since we need to round to the nearest cent (two decimal places), $0.655 becomes $0.66.

Step-by-Step Numerical Explanation

The first crucial step in determining the cost per pound of potatoes involves identifying the known values. We are given that a 10-pound sack of potatoes costs $6.55. These are the foundational pieces of information that we will use to solve the problem. Recognizing these values is essential because they directly inform our next steps in the calculation. Without clearly defined values, it is impossible to proceed accurately, highlighting the importance of understanding the information provided in the problem statement.

Once the known values are identified, the next logical step is to set up the division. To calculate the cost per pound, we must divide the total cost by the total weight. This mathematical operation is the core of our solution. Setting up the division correctly ensures that we are applying the appropriate method to find the unit price. The equation we need to solve is $6.55 ÷ 10. This setup clearly illustrates the relationship between the total cost, total weight, and the cost per unit, which is our target variable.

After setting up the division, the next critical action is to perform the actual division. Dividing $6.55 by 10 gives us the result $0.655. This result represents the cost of one pound of potatoes before rounding. The calculation provides a precise value that serves as the basis for our final answer. Performing the division accurately is essential to avoid errors and ensure the solution is mathematically sound. This step transforms the initial information into a usable figure that we can then refine to meet the problem's specific requirements.

Finally, the last step in our calculation process is to round the result to the nearest cent. The value we obtained from the division, $0.655, has three decimal places, but we need to express the cost in terms of dollars and cents, which means rounding to two decimal places. When rounding $0.655 to the nearest cent, we look at the third decimal place (the thousandths place). Since it is 5, we round up the second decimal place (the hundredths place). Therefore, $0.655 rounds up to $0.66. This final value represents the cost of one pound of potatoes, rounded to the nearest cent, fulfilling the problem's requirement.

Solution

Based on our calculations, one pound of potatoes would cost $0.66. Therefore, the correct answer is:

B) $.66

Importance of Understanding Unit Price

Understanding unit price is a crucial skill in personal finance and economics. It allows consumers to make informed decisions by comparing the cost of different products based on a standard unit of measure, such as per pound, per ounce, or per item. This makes it easier to determine which product offers the best value. Moreover, businesses use unit price calculations to set prices, evaluate profit margins, and understand market trends. By mastering this concept, individuals and organizations can effectively manage their resources and make economically sound choices.

Real-World Applications

In real-world scenarios, understanding unit price can significantly impact your budget and spending habits. For instance, when shopping for groceries, comparing the unit prices of different brands or package sizes can reveal which option is the most cost-effective. This is particularly useful when buying items in bulk versus individual servings. Recognizing the unit price allows you to evaluate whether the convenience of smaller packages justifies the higher cost per unit. Furthermore, understanding unit price extends beyond groceries to other purchases such as cleaning supplies, personal care products, and even larger items like electronics, where comparing prices per feature or capacity can be beneficial.

Moreover, businesses rely heavily on unit price analysis to optimize their pricing strategies and maintain competitiveness. By calculating the unit cost of their products, companies can determine appropriate retail prices that ensure profitability while remaining attractive to consumers. This analysis also helps in identifying cost-saving opportunities in production and supply chain management. For example, a manufacturer might discover that buying raw materials in larger quantities reduces the unit cost, thus improving overall profit margins. Understanding unit price, therefore, is a fundamental aspect of both personal and business financial management.

Common Mistakes to Avoid

When calculating unit price, there are several common mistakes that individuals often make, which can lead to incorrect purchasing decisions. One of the most frequent errors is failing to account for variations in package sizes. For example, a larger package might have a lower overall price but a higher unit price compared to a smaller package, making it a less economical choice. Another mistake is not considering promotional offers or discounts when calculating the unit price. A product on sale might appear cheaper at first glance, but calculating the unit price after the discount can reveal whether it truly offers better value.

Another pitfall is ignoring the actual weight or volume of the product. Sometimes, packaging can be misleading, and the advertised weight might not match the actual contents. Always check the net weight or volume printed on the package to ensure accurate unit price calculation. Additionally, individuals sometimes forget to round the unit price correctly. Rounding to the nearest cent is crucial for an accurate comparison, and incorrect rounding can skew the results. By being aware of these common mistakes, consumers can avoid overspending and make more informed purchasing decisions.

Conclusion

In summary, determining the cost of one pound of potatoes when a 10-pound sack costs $6.55 involves a straightforward division and rounding process. The correct answer is $0.66 per pound. This exercise highlights the importance of understanding unit price calculations in everyday life. By mastering this skill, consumers can make more informed purchasing decisions, ensuring they get the best value for their money. Businesses, too, can leverage unit price calculations to optimize pricing strategies and maintain a competitive edge in the market.