Frida's Third Child Unraveling The Birth Year Puzzle

Hey guys! Ever find yourself scratching your head over a tricky age-related puzzle? Well, let's dive into this fascinating problem involving Frida and her three children. We'll break it down step by step, using a bit of algebra and logical thinking, to pinpoint the birth year of Frida's youngest child.

Setting the Stage: Frida's Family Timeline

The problem states that Frida had her first child at 20, her second at 25, and her third seven years after the second. In 1996, the sum of her three children's ages was 83 years. Our mission? To discover the birth year of the third child. This is a classic age problem that requires us to think about the relationships between the children's ages and how they change over time. Before we jump into the calculations, let's establish some key variables to make our journey smoother. Let's call the age of the first child in 1996 'x'. This will be our starting point. Since the second child was born five years after the first, their age in 1996 would be 'x - 5'. Similarly, the third child, born seven years after the second (or 12 years after the first), would be 'x - 12' years old in 1996. Now that we have these variables defined, we can translate the information given in the problem into a mathematical equation. This equation will be the key to unlocking the solution. By carefully representing each child's age in terms of 'x', we can then use the information about the sum of their ages to solve for 'x'. Remember, the goal here is not just to find a number, but to understand the relationships between the ages and how they connect to the year of birth. Let's keep this in mind as we move forward in our calculations!

Cracking the Code: The Age Equation

Alright, let's get down to business and create the equation that will help us solve this puzzle. We know that the sum of the children's ages in 1996 was 83 years. We've also defined the ages of the first, second, and third children in terms of 'x'. So, we can write the equation as follows: x + (x - 5) + (x - 12) = 83. See how we've taken the ages of each child, represented by our variables, and added them together? This sum must equal the total of 83 years, as stated in the problem. Now, the next step is to simplify this equation. We need to combine like terms, which means adding together the 'x' terms and the constant numbers. On the left side of the equation, we have three 'x' terms, so they combine to become 3x. Then, we have -5 and -12, which combine to become -17. So, our simplified equation looks like this: 3x - 17 = 83. We're getting closer to finding the value of 'x'! This is where our algebra skills come into play. To isolate 'x', we need to get rid of the -17 on the left side. We do this by adding 17 to both sides of the equation. Remember, whatever we do to one side of the equation, we must do to the other to keep it balanced. This gives us 3x = 100. Now, just one more step to find 'x'! We need to divide both sides of the equation by 3. This will give us the value of 'x', which represents the age of the first child in 1996. Once we know the age of the first child, we can then easily calculate the ages of the other children and, more importantly, figure out the birth year of the third child.

Unveiling the Ages: Solving for 'x'

Okay, let's finish solving for 'x'! We've reached the point where we have the equation 3x = 100. To isolate 'x', as we discussed, we need to divide both sides of the equation by 3. When we do this, we get x = 100 / 3. Now, 100 divided by 3 is not a whole number; it's approximately 33.33. In the context of this problem, we need to think about what this decimal means. Can a person be 33.33 years old? Not really! This suggests that the age of the first child in 1996 was 33 years. While the exact calculation gives us a fraction, we need to consider the practical implications. A person's age is typically expressed as a whole number. So, let's use x = 33 as the age of the first child in 1996. Now that we have this crucial piece of information, we can determine the ages of the other children in 1996. Remember, the second child was born five years after the first, so in 1996, the second child would have been 33 - 5 = 28 years old. And the third child, born 12 years after the first, would have been 33 - 12 = 21 years old in 1996. We're on the verge of solving the puzzle! We've successfully calculated the ages of all three children in 1996. Now, we just need to use the age of the third child to figure out their birth year. This is the final step, and it's where everything comes together. Let's do it!

The Grand Finale: Pinpointing the Birth Year

Here we are, at the final stretch! We've determined that the third child was 21 years old in 1996. To find the birth year, we simply need to subtract the child's age from the year 1996. So, 1996 - 21 gives us 1975. Therefore, the third child was born in 1975. How cool is that? We've successfully navigated through the problem, using algebra and logical reasoning, to arrive at the answer. But before we celebrate too much, let's just double-check our work to make sure everything adds up correctly. We can quickly verify our solution by calculating the birth years of the other children as well. If the first child was 33 in 1996, they were born in 1996 - 33 = 1963. The second child, 28 in 1996, was born in 1996 - 28 = 1968. Now, let's look back at the original information. The problem stated that the second child was born five years after the first (1968 - 1963 = 5), and the third child was born seven years after the second (1975 - 1968 = 7). This confirms that our calculations are consistent with the given information. We did it! We've not only found the birth year of the third child but also verified our solution to ensure its accuracy. This is the beauty of problem-solving – the satisfaction of reaching the correct answer and the confidence of knowing you've done it right. So, there you have it, guys! Frida's third child was born in 1975. This puzzle reminds us that math isn't just about numbers and equations; it's about logic, reasoning, and the joy of discovery.

Repair Input Keyword

Find the birth year of Frida's third child, given that she had her first child at 20, her second at 25, her third 7 years after the second, and in 1996, the sum of her children's ages was 83.