La Edad De Jessica Es El Triple De La Edad De Brenda Hace 6 Años ¿Qué Edad Tiene Brenda?
Let's dive into a fascinating age-related problem where we need to figure out Brenda's current age. These types of puzzles often appear in math classes and even in real-life scenarios where we need to use logical deduction and basic algebra to solve them. So, grab your thinking caps, guys, and let's get started!
Setting Up the Equations: The Key to Solving the Puzzle
In this mathematical quest, the cornerstone of our approach lies in translating the word problem into the language of algebra. This involves carefully dissecting the given information and representing the unknowns with variables.
The first crucial piece of information is that Jessica's age is triple Brenda's age. To capture this relationship, we can introduce variables. Let's denote Brenda's current age as "B" and Jessica's current age as "J." The given information then translates to the equation J = 3B. This equation forms the bedrock of our solution, as it establishes a direct link between the two unknowns. It's like having a secret code that connects Jessica's and Brenda's ages.
The second vital clue revolves around their ages six years ago. We are told that the sum of their ages at that time was 28 years. To express this mathematically, we need to consider how ages change over time. Six years ago, Brenda's age would have been B - 6, and Jessica's age would have been J - 6. The sum of their ages six years ago can be written as (B - 6) + (J - 6) = 28. This equation provides us with another essential piece of the puzzle, linking their past ages to a specific sum. Think of it as a time capsule that reveals a snapshot of their ages in the past.
With these two equations in hand, we have laid the foundation for solving the problem. We have successfully transformed the word problem into a set of algebraic equations that we can manipulate and solve. This process of translating words into mathematical expressions is a fundamental skill in problem-solving, allowing us to apply the power of algebra to real-world scenarios. It's like having a translator that bridges the gap between everyday language and the precise language of mathematics.
Solving the Equations: Unveiling Brenda's Age
Now that we have our equations set up, it's time to put our algebraic skills to work and solve for Brenda's age. We have two equations:
- J = 3B
- (B - 6) + (J - 6) = 28
The most efficient way to solve this system of equations is through substitution. Since we know that J = 3B, we can substitute 3B for J in the second equation. This eliminates one variable and leaves us with an equation in terms of B only. It's like streamlining the problem by reducing the number of unknowns.
Substituting 3B for J in the second equation, we get:
(B - 6) + (3B - 6) = 28
Now, let's simplify this equation by combining like terms:
B - 6 + 3B - 6 = 28
4B - 12 = 28
To isolate the term with B, we add 12 to both sides of the equation:
4B - 12 + 12 = 28 + 12
4B = 40
Finally, to solve for B, we divide both sides of the equation by 4:
4B / 4 = 40 / 4
B = 10
So, we have found that Brenda's current age, represented by B, is 10 years old. It's like cracking the code and revealing the hidden answer. But, just to be sure, let's calculate Jessica's age as well. Since J = 3B, and B = 10, then Jessica's age is:
J = 3 * 10 = 30
Therefore, Jessica is currently 30 years old. It's like connecting the dots and getting the full picture. To verify our solution, we can plug these values back into the original equations. The first equation, J = 3B, holds true because 30 = 3 * 10. For the second equation, six years ago, Brenda was 10 - 6 = 4 years old, and Jessica was 30 - 6 = 24 years old. The sum of their ages was 4 + 24 = 28, which confirms our solution. It's like double-checking our work to ensure accuracy.
The Answer: Brenda's Age Revealed
After meticulously setting up the equations, substituting variables, and simplifying, we've arrived at the solution. Brenda is currently 10 years old. This was a classic algebra problem that required us to translate word clues into mathematical equations, and then solve those equations. These are fundamental skills in math and can be applied to many real-life situations. It's like completing a puzzle, each step leading us closer to the final solution. Remember, guys, the key to solving these problems is to break them down into smaller, manageable steps. Now you've got the skills to tackle similar challenges. So go forth and conquer those math problems!