Solución de problemas con Ecuaciones de Primer Grado | Ejemplo 5

Summary

In this educational video, the instructor demonstrates how to solve a first-degree equation problem involving the ages of a father and son. Initially, the problem is approached logically, where the solution is found by adding years to their current ages to determine when the father’s age will be three times that of the son’s. The instructor then solves the problem algebraically for practice, showing how to set up and solve equations. Additionally, the video includes another example involving the ages of two brothers, providing step-by-step instructions for solving both types of problems with both logical reasoning and algebraic equations.

Takeaways

• 😀 Logical problem-solving is encouraged before jumping into equations. This helps with better understanding and simplifying the process.
• 😀 Start by estimating the solution logically. In this case, we guessed how many years it might take for the father’s age to be three times the son’s.
• 😀 The first estimate showed that 10 years was too long, as the father's age became much higher than the triple of the son's age.
• 😀 The correct estimate was 5 years, when the father will be 42 and the son will be 14, making the father’s age three times that of the son.
• 😀 For algebraic solutions, always start by defining a variable (in this case, 'a') to represent the number of years in the future.
• 😀 Set up the equation where the father’s age in 'a' years is equal to three times the son’s age in 'a' years. The equation was: 37 + a = 3 * (9 + a).
• 😀 Simplify the algebraic equation by distributing and solving step-by-step to isolate the variable 'a'.
• 😀 After solving the equation, it was found that 'a = 5', meaning that the solution is 5 years.
• 😀 The final answer was that in 5 years, the father's age would be 42 and the son’s age would be 14, satisfying the condition.
• 😀 This approach shows how both logical reasoning and algebraic equations can be used together to solve age-related problems effectively.

Q & A

What is the first recommendation the speaker gives when solving these types of problems?

The speaker recommends first trying to solve the problem logically without using equations. This method often leads to finding the answer, and then you can use equations to practice and reinforce your skills.

What was the specific math problem presented in the video?

The problem involved a father who is 37 years old and his son, who is 9 years old. The question asks, 'In how many years will the father's age be three times the son's age?'

How did the speaker initially attempt to solve the problem logically?

The speaker started by assuming a number of years (e.g., 10 years) and checked if the father's age would be three times the son's age. After testing different values, they found that in 5 years, the father's age would indeed be three times the son's age.

What conclusion did the speaker reach after testing different years?

After testing 10 years and 5 years, the speaker concluded that in 5 years, the father’s age would be three times the son's age.

How did the speaker suggest solving the problem using algebraic equations?

The speaker defined a variable (a) for the number of years after which the father’s age will be three times the son’s age. They then set up an equation to express the father’s age (37 + a) as being three times the son's age (3 * (9 + a)), and solved the equation algebraically.

What equation did the speaker form to represent the situation?

The equation formed was 37 + a = 3 * (9 + a), where 'a' represents the number of years after which the father’s age will be three times the son’s age.

What was the process to solve the equation?

The speaker distributed the 3 in the equation, resulting in 37 + a = 27 + 3a. Then, they moved the terms involving 'a' to one side and the constants to the other side, simplifying to 10 = 2a. Dividing both sides by 2, they found a = 5.

What does the solution 'a = 5' represent in the context of the problem?

'a = 5' means that in 5 years, the father's age will be three times the son's age.

What additional detail did the speaker provide after solving the equation?

After solving the equation, the speaker verified the solution by calculating the ages of the father and son in 5 years. The father will be 42 years old, and the son will be 14 years old, confirming that the father's age is three times the son's age.

What other exercise did the speaker suggest for practice?

The speaker suggested another exercise involving two brothers, where their ages sum to 34 years, and one brother is 4 years older than the other. The goal was to calculate their ages using algebraic equations.