Solving Chicken Quantity Problem Algebraically
In this mathematical problem, we are presented with a scenario involving two individuals, Kuria and Mutua, and the number of chickens they possess. The problem requires us to determine the total number of chickens owned by both individuals, given that Kuria has (y+4) chickens and Mutua has thrice as many chickens as Kuria. To solve this problem effectively, we need to utilize algebraic expressions and apply the principles of arithmetic operations. This exploration will delve into the step-by-step solution, ensuring clarity and comprehension for readers of all backgrounds. Let's embark on this mathematical journey to unravel the solution and understand the underlying concepts.
Defining the Variables
To begin, let's define the variables involved in this problem. We are told that Kuria has (y+4) chickens. This means that the number of chickens Kuria possesses is represented by the algebraic expression 'y+4', where 'y' is a variable representing an unknown quantity. This algebraic representation allows us to express the quantity of chickens Kuria owns in a concise and mathematical manner. Understanding how to define variables is crucial in mathematics as it allows us to translate real-world scenarios into mathematical expressions, making it easier to solve problems. The variable 'y' in this context can represent any numerical value, and the expression 'y+4' will always represent the number of chickens Kuria has, which is four more than the value of 'y'. This concept of using variables and expressions is fundamental to algebra and problem-solving in mathematics.
Determining Mutua's Chickens
Next, we need to determine the number of chickens Mutua has. The problem states that Mutua has thrice as many chickens as Kuria. This means that Mutua has three times the number of chickens that Kuria has. Since Kuria has (y+4) chickens, we can express the number of chickens Mutua has as 3 * (y+4). To simplify this expression, we need to apply the distributive property of multiplication over addition. This property states that a * (b + c) = a * b + a * c. Applying this property to our expression, we get 3 * y + 3 * 4, which simplifies to 3y + 12. Therefore, Mutua has (3y + 12) chickens. This step is crucial as it translates the given information into an algebraic expression that can be used to find the total number of chickens. Understanding and applying the distributive property is essential for simplifying algebraic expressions and solving mathematical problems.
Calculating the Total Chickens
Now that we know the number of chickens Kuria and Mutua have individually, we can calculate the total number of chickens they have altogether. Kuria has (y+4) chickens, and Mutua has (3y+12) chickens. To find the total, we need to add these two expressions together: (y+4) + (3y+12). To add these expressions, we combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, 'y' and '3y' are like terms, and '4' and '12' are like terms. Adding the 'y' terms, we have y + 3y = 4y. Adding the constant terms, we have 4 + 12 = 16. Therefore, the total number of chickens is 4y + 16. This algebraic expression represents the combined number of chickens owned by Kuria and Mutua. Understanding how to combine like terms is a fundamental skill in algebra and is essential for simplifying expressions and solving equations.
Selecting the Correct Answer
Based on our calculations, the total number of chickens Kuria and Mutua have altogether is represented by the expression 4y + 16. This matches option B in the given choices. Therefore, the correct answer is B. 4y+16. The process of arriving at this answer involved several key steps, including defining variables, applying the distributive property, and combining like terms. Each of these steps is crucial in solving algebraic problems and demonstrates the importance of understanding fundamental mathematical concepts. By breaking down the problem into smaller, manageable steps, we can systematically arrive at the correct solution. This problem highlights the practical application of algebra in solving real-world scenarios.
Conclusion
In conclusion, this problem demonstrates how algebraic expressions can be used to represent and solve real-world scenarios. By carefully defining variables, applying mathematical properties, and simplifying expressions, we were able to determine the total number of chickens owned by Kuria and Mutua. The solution, 4y + 16, accurately represents the combined quantity of chickens and highlights the power of algebra in problem-solving. This exercise reinforces the importance of understanding algebraic concepts and their applications in everyday situations. The ability to translate word problems into mathematical expressions is a valuable skill that can be applied in various fields, from finance to engineering. The systematic approach used to solve this problem serves as a template for tackling similar mathematical challenges.
Final Thoughts
The problem we tackled today underscores the significance of algebra in our daily lives. From simple scenarios like counting chickens to complex financial calculations, algebra provides the tools and methods to solve a wide array of problems. The key takeaway is the ability to break down a problem into manageable steps, define variables, and apply relevant mathematical properties. The use of algebraic expressions allows us to represent unknown quantities and relationships in a concise and precise manner. The distributive property, combining like terms, and simplifying expressions are fundamental skills that are essential for success in algebra and beyond. By mastering these concepts, individuals can confidently approach mathematical challenges and find solutions effectively. This problem serves as a reminder that mathematics is not just an academic subject but a practical tool that can be used to make sense of the world around us.
In summary, the correct answer is B. 4y+16, which represents the total number of chickens Kuria and Mutua have altogether. This was achieved by first understanding the problem, defining the variables, applying the distributive property, combining like terms, and simplifying the expression. This systematic approach is crucial for solving algebraic problems and can be applied to various real-world scenarios. Understanding and applying these mathematical concepts empowers individuals to solve problems confidently and effectively.
