Solving Math Problems Calculating Profit, Algebraic Equations And Order Of Operations

To determine the selling price of a chair that yields a 40% profit on a GHe 25.00 cost, we need to delve into the realms of percentage calculations and profit margins. This involves a step-by-step approach to first calculate the desired profit amount and then add it to the original cost. Understanding these fundamental concepts of cost price, profit percentage, and selling price is crucial for any business or individual engaged in buying and selling. Let's embark on this mathematical journey to unravel the solution.

First, we need to calculate the profit amount. The profit is 40% of the cost price, which is GHe 25.00. To find 40% of GHe 25.00, we can convert the percentage to a decimal by dividing it by 100 (40/100 = 0.40). Then, we multiply this decimal by the cost price: 0.40 * GHe 25.00. This calculation gives us the profit amount in GHe. This is a straightforward application of percentage calculations, a cornerstone of many financial and mathematical problems.

Next, perform the multiplication: 0. 40 * GHe 25. 00 = GHe 10. 00. This means the desired profit is GHe 10. 00. The calculation highlights the direct relationship between the profit percentage and the actual profit amount earned on the sale of the chair. The higher the profit percentage, the greater the profit earned, assuming the cost price remains constant.

Now that we know the profit amount, we can calculate the selling price. The selling price is the sum of the cost price and the profit. So, we add the cost price of GHe 25.00 to the profit of GHe 10.00: GHe 25.00 + GHe 10.00. This addition will give us the final selling price required to achieve a 40% profit margin. This step underscores the fundamental accounting principle that selling price covers both the initial cost and the desired profit.

Adding these two amounts together, we get GHe 25. 00 + GHe 10. 00 = GHe 35. 00. Therefore, the chair should be sold for GHe 35. 00 to make a 40% profit. This final selling price ensures that the carpenter not only recovers the cost of materials and labor but also earns a satisfactory profit for their efforts. Understanding how to calculate profit margins is essential for businesses to operate sustainably and achieve their financial goals. This example demonstrates a practical application of basic arithmetic and percentage calculations in a real-world scenario.

In conclusion, to achieve a 40% profit on a chair that costs GHe 25. 00 to make, the chair should be sold for GHe 35. 00. This calculation involves finding the profit amount (40% of GHe 25. 00) and adding it to the original cost. This problem illustrates the importance of understanding profit margins and percentage calculations in business and everyday financial transactions. The correct answer, therefore, is B. GHe 35.00.

To find the value of 'y' in the equation 0. 03 * y = 2. 4, we need to apply the fundamental principles of algebraic equations. This involves isolating the variable 'y' on one side of the equation. The key operation here is division, as we need to undo the multiplication by 0. 03. This is a classic example of solving a linear equation, a cornerstone of algebra and a skill that is crucial in various mathematical and scientific contexts. Understanding the properties of equations and how to manipulate them is essential for solving a wide range of problems.

The equation we are given is 0. 03 * y = 2. 4. This means that 0. 03 multiplied by 'y' equals 2. 4. To isolate 'y', we need to perform the inverse operation of multiplication, which is division. We will divide both sides of the equation by 0. 03. This ensures that the equation remains balanced, a critical principle in algebra. Any operation performed on one side of the equation must also be performed on the other side to maintain equality.

Dividing both sides by 0. 03, we get (0. 03 * y) / 0. 03 = 2. 4 / 0. 03. This step effectively cancels out the 0. 03 on the left side of the equation, leaving 'y' by itself. This process highlights the importance of inverse operations in solving equations. Multiplication and division are inverse operations, just like addition and subtraction.

Now, we need to perform the division on the right side of the equation: 2. 4 / 0. 03. To make this division easier, we can multiply both the dividend (2. 4) and the divisor (0. 03) by 100. This will eliminate the decimal points, making the division simpler. Multiplying both numbers by the same value does not change the result of the division, a crucial property of fractions and division.

Multiplying both 2. 4 and 0. 03 by 100, we get 240 / 3. This is a much simpler division problem to solve. This transformation illustrates a common technique used to simplify division problems involving decimals. By multiplying both the dividend and divisor by a power of 10, we can often convert the problem into one involving whole numbers.

Performing the division, 240 / 3 = 80. Therefore, the value of 'y' is 80. This result means that if we substitute 80 for 'y' in the original equation (0. 03 * y = 2. 4), the equation will hold true. This is a good way to check the solution to an equation – by substituting the value back into the original equation and verifying that both sides are equal.

In conclusion, the value of 'y' in the equation 0. 03 * y = 2. 4 is 80. This was found by dividing both sides of the equation by 0. 03 and simplifying the resulting division. The correct answer, therefore, is D. 80.0. This problem demonstrates the application of fundamental algebraic principles in solving for an unknown variable.

To solve this mathematical expression, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule dictates the sequence in which mathematical operations should be performed to ensure a consistent and accurate result. In this case, we first need to evaluate the exponent, then perform the subtraction within the parentheses, and finally, perform the multiplication. This problem highlights the importance of adhering to the order of operations in mathematics, a fundamental concept that ensures clarity and consistency in mathematical calculations. Let's break down the steps one by one.

First, we need to evaluate the exponent, which is 8^2. This means 8 raised to the power of 2, or 8 multiplied by itself (8 * 8). Exponents indicate repeated multiplication, and understanding how to evaluate them is crucial for various mathematical concepts, including algebra, calculus, and more. The concept of exponents is a fundamental building block in mathematics.

Calculating 8 * 8, we get 64. So, 8^2 = 64. Now, we can substitute this value back into the original expression: (64 - 7). This step simplifies the expression, reducing the complexity of the problem and bringing us closer to the final solution. Substituting calculated values back into the expression is a common technique used in mathematics to solve complex problems in a step-by-step manner.

Next, we need to perform the subtraction within the parentheses: 64 - 7. This is a straightforward subtraction operation. The result of this subtraction will give us the value inside the parentheses, which we can then use for the final multiplication step. Parentheses often group operations that need to be performed before others, as dictated by the order of operations.

Subtracting 7 from 64, we get 57. So, (64 - 7) = 57. This simplifies the expression to a single number. Now that we have evaluated the expression within the parentheses, we are ready to move on to the final step, which involves multiplication. This step-by-step approach is essential for accurately solving mathematical expressions.

Finally, we need to multiply 57. If there was an additional number to perform multiplication. But the question only request to simplify (8^2 - 7) which result is 57. Therefore, the result of the calculation is 57. This concludes the simplification of the given expression. The order of operations has been followed meticulously to arrive at the correct answer. This problem underscores the importance of understanding and applying mathematical rules correctly.

In conclusion, the result of simplifying the expression (8^2 - 7) is 57. This was achieved by following the order of operations (PEMDAS), first evaluating the exponent, then performing the subtraction within the parentheses. This problem highlights the importance of understanding and applying mathematical rules correctly. This problem underscores the importance of understanding and applying mathematical rules correctly.