Calculating Costs Of Bananas, Candles, Pineapples, And T-shirts A Math Guide

When dealing with basic arithmetic problems, it's essential to break down the given information into smaller, manageable parts. In this case, we're presented with a classic problem involving the price of bananas. We know that a dozen bananas, which is equivalent to 12 bananas, costs $18. The goal is to determine the cost of just 4 bananas. To solve this, we can use a simple method called proportion. We can establish the ratio of the number of bananas to their cost. So, if 12 bananas cost $18, we can write this as a ratio: 12 bananas / $18. To find the cost of 1 banana, we divide the total cost by the number of bananas: $18 / 12 = $1.50 per banana. Now that we know the cost of a single banana, we can easily calculate the cost of 4 bananas. We multiply the cost of one banana ($1.50) by the number of bananas we want to buy (4): $1.50 * 4 = $6. Therefore, the cost of 4 bananas is $6. This type of problem highlights the importance of understanding unit prices and how they can be used to calculate the cost of different quantities. By breaking down the problem into smaller steps, we can arrive at the solution more easily. This concept is not only applicable to bananas but also to a wide range of goods and services. The ability to calculate unit prices and apply them to different quantities is a valuable skill in everyday life, from grocery shopping to budgeting. Furthermore, this problem serves as a foundation for more complex mathematical concepts such as ratios, proportions, and algebraic equations. As we progress in mathematics, we encounter problems that require us to manipulate these concepts in more sophisticated ways. However, the underlying principles remain the same: break down the problem into smaller parts, identify the relevant information, and apply the appropriate operations.

In this problem, we shift our focus from fruits to candles. We are given that a score of candles costs $30. It's important to know what a "score" represents in terms of quantity. A score is a unit of measurement that equals 20. So, a score of candles means we have 20 candles. The question asks us to find the cost of one candle. Similar to the previous problem, we can use the concept of unit price to solve this. We know the total cost of 20 candles is $30. To find the cost of one candle, we simply divide the total cost by the number of candles: $30 / 20 = $1.50 per candle. Therefore, the cost of one candle is $1.50. This problem reinforces the importance of understanding different units of measurement and how they relate to quantity. In this case, knowing that a score equals 20 is crucial to solving the problem correctly. Without this knowledge, we would not be able to determine the cost of a single candle. This problem also highlights the versatility of unit price calculations. We can use the same principle to find the cost of individual items whether we are dealing with bananas, candles, or any other product. The ability to calculate unit prices allows us to compare the cost of different items and make informed purchasing decisions. For example, if we were buying candles in bulk, we could use the unit price to determine whether it is more cost-effective to buy a score of candles or individual candles. This type of analysis is essential for budgeting and managing expenses effectively. Furthermore, this problem can be extended to more complex scenarios involving discounts, sales tax, and other factors that affect the final price of an item. By mastering the basic concept of unit price, we can tackle these more challenging problems with confidence.

Next, we consider the cost of pineapples. We are told that the cost of one pineapple is $5. The question asks us to find the cost of 12 pineapples. This problem is a straightforward application of multiplication. We know the cost of one pineapple and we want to find the cost of multiple pineapples. To do this, we simply multiply the cost of one pineapple by the number of pineapples we want to buy: $5 * 12 = $60. Therefore, the cost of 12 pineapples is $60. This problem illustrates the fundamental concept of multiplication as repeated addition. We are essentially adding the cost of one pineapple ($5) to itself 12 times. Multiplication provides a more efficient way to perform this calculation. This problem also reinforces the importance of paying attention to the units involved in the calculation. In this case, we are multiplying dollars per pineapple by the number of pineapples. The result is the total cost in dollars. Understanding the units helps us ensure that we are performing the calculation correctly and that the answer makes sense in the context of the problem. This problem can be extended to more complex scenarios involving bulk discounts or sales tax. For example, we might be offered a discount if we buy more than a certain number of pineapples. Or, we might need to calculate the sales tax on the total cost of the pineapples. By mastering the basic concept of multiplication, we can tackle these more challenging problems with ease. Furthermore, this problem can be used to introduce the concept of functions. We can define a function that takes the number of pineapples as input and returns the total cost as output. This function would simply multiply the number of pineapples by the cost per pineapple. This concept is essential for understanding more advanced mathematical topics such as calculus and linear algebra.

Finally, we address the cost of t-shirts. We are given that the price of 5 t-shirts is $350. The question asks us to find the rate, which in this context refers to the cost per t-shirt. To find the rate, we need to divide the total cost by the number of t-shirts. So, we divide $350 by 5: $350 / 5 = $70 per t-shirt. Therefore, the rate or cost of one t-shirt is $70. This problem emphasizes the concept of rate as a ratio of two quantities. In this case, the rate is the ratio of the total cost to the number of t-shirts. Understanding rates is essential for comparing the cost of different items and making informed purchasing decisions. For example, if we were comparing the price of t-shirts from different stores, we would want to compare the rate or cost per t-shirt. This would allow us to determine which store offers the best deal. This problem also highlights the importance of paying attention to the units involved in the calculation. In this case, we are dividing dollars by the number of t-shirts. The result is the cost in dollars per t-shirt. Understanding the units helps us ensure that we are performing the calculation correctly and that the answer makes sense in the context of the problem. This problem can be extended to more complex scenarios involving discounts, sales tax, and shipping costs. For example, we might be offered a discount if we buy more than a certain number of t-shirts. Or, we might need to calculate the sales tax on the total cost of the t-shirts. By mastering the basic concept of rate, we can tackle these more challenging problems with confidence. Furthermore, this problem can be used to introduce the concept of unit rates. A unit rate is a rate where the denominator is 1. In this case, the unit rate is $70 per 1 t-shirt. Unit rates are useful for comparing different rates and making calculations.

In conclusion, these problems demonstrate fundamental mathematical concepts such as proportion, unit price, multiplication, and rate. By understanding these concepts, we can solve a wide range of everyday problems involving costs and quantities. These skills are essential for budgeting, shopping, and making informed financial decisions. Furthermore, these problems serve as a foundation for more advanced mathematical topics that we will encounter in our academic and professional lives.