The Triple Of Bruno's Age, Increased By 10, Is 25. How Old Is Bruno?
This article aims to delve into the intriguing mathematical puzzle presented: "El triple de la edad de Bruno, aumentando en 10 es 25. ¿Que edad tiene Bruno?" which translates to "Three times Bruno's age, increased by 10, is 25. What is Bruno's age?" We will meticulously dissect this problem, employing algebraic principles to unravel the solution. Our approach will prioritize clarity and comprehensibility, ensuring that readers of all mathematical backgrounds can grasp the underlying concepts and arrive at the correct answer. Beyond the immediate solution, we will also explore the broader implications of such problems in fostering analytical thinking and problem-solving skills. Let's embark on this mathematical journey together, unraveling the mystery of Bruno's age and gaining valuable insights into the world of algebra.
Decoding the Equation
To decode the equation and embark on our quest to determine Bruno's age, we must first translate the given word problem into a concise algebraic expression. This crucial step involves identifying the unknown variable, which in this case is Bruno's age. Let's denote Bruno's age as "x". Now, we can systematically break down the problem statement: "El triple de la edad de Bruno" translates to 3 multiplied by Bruno's age, or 3x. "Aumentando en 10" signifies adding 10 to the previous expression, resulting in 3x + 10. Finally, "es 25" indicates that the entire expression is equal to 25. Therefore, the complete algebraic equation representing the problem is 3x + 10 = 25. This equation serves as the foundation for our subsequent steps in solving for Bruno's age. By meticulously translating the word problem into a symbolic representation, we have laid the groundwork for applying algebraic techniques to arrive at the solution. This process underscores the power of algebra in transforming complex scenarios into manageable mathematical expressions, paving the way for problem-solving and analytical reasoning.
Isolating the Variable
With the equation 3x + 10 = 25 firmly established, our next crucial step involves isolating the variable 'x', which represents Bruno's age. This process entails strategically manipulating the equation to bring 'x' to one side, while all other terms are moved to the opposite side. To achieve this, we must first address the constant term, which is 10. Since 10 is being added to 3x, we employ the inverse operation, which is subtraction. By subtracting 10 from both sides of the equation, we maintain the equality while effectively neutralizing the +10 on the left side. This yields the intermediate equation 3x = 15. Now, the variable term, 3x, is closer to being isolated. However, 'x' is still being multiplied by 3. To undo this multiplication, we again resort to the inverse operation, which is division. By dividing both sides of the equation by 3, we isolate 'x' completely. This final step results in the solution x = 5. Therefore, through the systematic application of inverse operations, we have successfully isolated the variable and determined that Bruno's age is 5. This methodical approach underscores the elegance and precision of algebraic techniques in solving equations and extracting unknown values.
Solving for Bruno's Age
Having successfully isolated the variable 'x', we have arrived at the solution: x = 5. This signifies that Bruno's age is 5. To ensure the validity of our solution, it is prudent to substitute this value back into the original equation, 3x + 10 = 25. By replacing 'x' with 5, we obtain 3(5) + 10 = 25. Evaluating the left side of the equation, we find 15 + 10 = 25, which simplifies to 25 = 25. This confirms that our solution is indeed correct, as the equation holds true when x = 5. Therefore, we can confidently state that Bruno is 5 years old. This process of verification underscores the importance of checking solutions in mathematical problem-solving, ensuring accuracy and reinforcing understanding. Furthermore, the successful determination of Bruno's age highlights the power of algebraic techniques in unraveling real-world scenarios and extracting meaningful information from seemingly complex problems. The ability to translate word problems into algebraic equations and solve for unknowns is a fundamental skill with wide-ranging applications in various fields.
Verifying the Solution
Verifying the solution is a critical step in the problem-solving process, as it ensures the accuracy and validity of our answer. In this case, we have determined that Bruno's age is 5. To verify this solution, we substitute x = 5 back into the original equation, 3x + 10 = 25. This substitution yields 3(5) + 10 = 25. Now, we simplify the left side of the equation following the order of operations. First, we perform the multiplication: 3 multiplied by 5 equals 15. This gives us 15 + 10 = 25. Next, we perform the addition: 15 plus 10 equals 25. This results in the equation 25 = 25, which is a true statement. Since the equation holds true when x = 5, we can confidently conclude that our solution is correct. This verification process not only confirms the accuracy of our answer but also reinforces our understanding of the problem and the algebraic techniques employed. By meticulously checking our work, we minimize the risk of errors and build confidence in our problem-solving abilities. Furthermore, the habit of verifying solutions is a valuable skill that extends beyond mathematics, promoting critical thinking and attention to detail in all aspects of life.
Conclusion
In conclusion, we have successfully navigated the mathematical puzzle presented, unraveling the mystery of Bruno's age. By meticulously translating the word problem into an algebraic equation, 3x + 10 = 25, we laid the foundation for our solution. Through the strategic application of inverse operations, we isolated the variable 'x', representing Bruno's age, and arrived at the solution x = 5. To ensure the accuracy of our result, we diligently verified the solution by substituting x = 5 back into the original equation, confirming its validity. Therefore, we confidently conclude that Bruno is 5 years old. This journey through problem-solving underscores the power of algebra in transforming real-world scenarios into manageable mathematical expressions. The ability to translate word problems into equations, manipulate them to isolate unknowns, and verify solutions is a fundamental skill with broad applications. Beyond the specific solution to this problem, the process highlights the importance of analytical thinking, attention to detail, and systematic problem-solving strategies. These skills are not only valuable in mathematics but also in various aspects of life, fostering critical thinking and decision-making abilities. As we conclude this exploration, we recognize the significance of mathematical literacy in empowering individuals to tackle challenges, make informed decisions, and navigate the complexities of the world around them.