Solving Mathematics Problems Step By Step

In tackling mathematical problems, it's crucial to systematically analyze the information provided and apply the appropriate concepts and formulas to arrive at the correct solution. For the first problem, the exact question or context is missing, making it impossible to provide a definitive answer. However, we can discuss general strategies for solving similar problems. If the question involves solving for an unknown variable (let's say 'K'), we would typically need an equation or relationship that includes 'K'. This equation might come from a word problem, a geometric figure, or a given formula. Once we have the equation, we can use algebraic manipulation to isolate 'K' on one side and find its value. For instance, if the equation were 2K + 5 = 28, we would subtract 5 from both sides to get 2K = 23, and then divide both sides by 2 to find K = 11.5. Therefore, if the options provided (K 11.48 and K 12.30) are close to our calculated value, it suggests that the original problem might involve a similar algebraic process or an approximation. It's essential to carefully review the problem statement and identify the key information needed to set up the equation. Understanding the underlying mathematical principles is paramount to accurately solve such problems. Consider different mathematical concepts like arithmetic operations, algebraic equations, geometric properties, or trigonometric relationships that might apply to the unknown problem. Without the specific question, we can only speculate, but the general approach involves setting up an equation and solving for the unknown variable. Make sure to double-check your calculations and ensure the solution makes sense in the context of the problem. Pay close attention to the units if the problem involves real-world quantities. By following these steps, you can systematically approach and solve a wide range of mathematical problems involving unknown values. Remember, practice and familiarity with different types of problems are key to improving your problem-solving skills.

To calculate the investment value after 5 years with compound interest, we utilize the compound interest formula. Compound interest is the interest calculated on the principal plus the accumulated interest. This differs from simple interest, where interest is calculated only on the principal amount. The formula for compound interest is: A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial investment), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed for. In this specific problem, we have P = K 2000, r = 5% or 0.05, n = 1 (compounded annually), and t = 5 years. Plugging these values into the formula, we get: A = 2000 (1 + 0.05/1)^(1*5) = 2000 (1.05)^5. Now we calculate (1.05)^5, which is approximately 1.27628. Multiplying this by the principal amount, we have: A = 2000 * 1.27628 ≈ K 2552.56. Therefore, the investment value after 5 years is approximately K 2552.56. The correct answer among the given options is D. K 2552.56. This calculation demonstrates the power of compound interest, where the investment grows exponentially over time. It's crucial to understand the parameters in the compound interest formula and how they affect the final amount. For example, compounding more frequently (e.g., monthly or daily) will result in a slightly higher final amount due to the more frequent addition of interest. Always ensure you are using the correct formula and substituting the values accurately. When dealing with financial calculations, it's also beneficial to understand concepts like present value, future value, and the time value of money. These concepts help in making informed financial decisions and understanding the growth potential of investments over time. In summary, the compound interest formula is a powerful tool for calculating the future value of an investment, and understanding its components is essential for financial planning.

Determining the sale price after a discount involves a straightforward calculation. The core concept here is to understand the percentage discount and how it reduces the original marked price. Let's break down the process. First, the discount is given as a percentage of the marked price. In this case, a discount of 30% was allowed on a marked price. To find the amount of the discount, we multiply the marked price by the discount percentage (expressed as a decimal). For example, if the marked price was K 100, the discount amount would be 30% of K 100, which is (30/100) * K 100 = K 30. Once we have calculated the discount amount, we subtract it from the marked price to find the sale price. So, in the previous example, the sale price would be K 100 - K 30 = K 70. This sale price represents the amount a customer would actually pay for the item after the discount is applied. If the original problem provided a specific marked price, we would follow these steps to find the sale price. For instance, if the marked price was K 500, the discount would be 30% of K 500, which is (30/100) * K 500 = K 150. Subtracting the discount from the marked price, the sale price would be K 500 - K 150 = K 350. Understanding percentage discounts is not only essential in mathematical problems but also in real-world scenarios such as shopping and budgeting. It's also important to differentiate between a discount and a markup. A discount reduces the price, while a markup increases the price. Both are calculated as a percentage of the original price, but they have opposite effects. In conclusion, calculating the sale price after a discount involves finding the discount amount (by multiplying the marked price by the discount percentage) and then subtracting that amount from the marked price. This simple yet crucial calculation is a fundamental skill in both mathematics and everyday life. Applying this skill accurately ensures you can correctly determine the final price of an item after a discount.