Age Problem: Alina Is 4 Times Older Than Mihai

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Age Problem: Alina is 4 Times Older Than Mihai

Hey guys! Let's dive into a cool math problem today. We're going to figure out how old Alina is, given that she and Mihai are 95 years old together, and Alina is four times older than Mihai. Sounds like fun, right? So, buckle up, and let’s get started!

Understanding the Problem

To solve this, first, we need to understand the information. The core of the problem lies in translating the words into mathematical relationships. We know two crucial facts:

  1. Alina and Mihai's combined age: This means if we add Alina's age and Mihai's age, we get 95 years.
  2. Alina's age relative to Mihai's: This tells us Alina is four times older than Mihai. This is a multiplicative relationship, meaning Alina's age is Mihai's age multiplied by four.

With these two pieces of information, we can set up a mathematical model to solve the problem. It's like having a secret code, and now we have the clues to crack it. Think of it as a puzzle where the numbers are the pieces, and we need to fit them together to find the answer. It's all about turning a word problem into a solvable equation.

Setting Up the Equation

Okay, let’s translate these facts into an equation. This is where the magic happens! We’ll use algebra to represent the unknowns. Let's say Mihai's age is “M” (a common way to represent an unknown in math). Since Alina is four times older than Mihai, we can say Alina’s age is “4M”.

Now, we know their combined age is 95 years. This gives us our main equation:

M + 4M = 95

See how we took the words and turned them into something we can actually solve? This is the power of math – taking real-world situations and making them logical and solvable. Now, let’s simplify this equation. We can combine the “M” terms because they’re like terms. Think of it as adding apples – one apple plus four apples equals five apples. So, we’re on our way to cracking the puzzle!

Solving for Mihai's Age

Alright, let's simplify the equation we set up earlier: M + 4M = 95. When we combine the like terms (M and 4M), we get 5M = 95. Now, the goal is to isolate M, which means we want to get M by itself on one side of the equation. To do this, we need to undo the multiplication. Remember, in math, we often use the opposite operation to solve for unknowns.

Since M is being multiplied by 5, we need to divide both sides of the equation by 5. This keeps the equation balanced, which is super important. It’s like a scale – whatever you do to one side, you have to do to the other to keep it even. So, we divide 5M by 5, which gives us M, and we divide 95 by 5. When you do the math, 95 divided by 5 equals 19. Therefore, M = 19. This means Mihai is 19 years old! We've taken the first big step in solving our problem.

Calculating Alina's Age

Now that we know Mihai's age, figuring out Alina's age is the next logical step. Remember, the problem stated that Alina is four times older than Mihai. We've already established that Mihai is 19 years old. So, to find Alina's age, we simply need to multiply Mihai's age by 4. This is a straightforward calculation, and it directly uses the relationship given in the problem. Multiplying 19 (Mihai's age) by 4 will give us Alina's age.

Let's do the math: 19 multiplied by 4 equals 76. Therefore, Alina is 76 years old. See how neatly the problem unfolds once we have the basic pieces? We used Mihai’s age as a stepping stone to find Alina’s age. This kind of problem-solving is like detective work, where each clue leads you closer to the final answer.

Verifying the Solution

So, we’ve figured out that Mihai is 19 years old and Alina is 76 years old. But before we declare victory, it’s a good idea to double-check our work. This is an essential step in problem-solving – ensuring that our solution makes sense in the context of the original problem. There are two main conditions we need to verify:

  1. Combined Age: Does the sum of their ages equal 95? We need to add Mihai's age (19) and Alina's age (76) to see if it totals 95. If it doesn't, we know there's a mistake somewhere.
  2. Age Relationship: Is Alina four times older than Mihai? We already used this to calculate Alina's age, but it’s worth confirming. We can divide Alina's age (76) by Mihai's age (19) and see if we get 4. If we do, that confirms our calculation aligns with the problem's condition.

By verifying these two conditions, we can be confident that our solution is correct. Let’s put these numbers to the test!

Checking the Math

Let's start by verifying the combined age. We need to add Mihai's age, which is 19, to Alina's age, which is 76. So, 19 + 76 equals 95. This matches the information given in the problem that their combined age is indeed 95 years. Great! Our first condition is met.

Now, let's check the age relationship. The problem states that Alina is four times older than Mihai. To verify this, we'll divide Alina's age by Mihai's age. So, we divide 76 by 19. When you do the math, 76 divided by 19 equals 4. This confirms that Alina is indeed four times older than Mihai. We’ve nailed the second condition!

Since both conditions are met – their combined age is 95, and Alina is four times older than Mihai – we can confidently say that our solution is correct. This verification step is super important because it ensures we haven't made any calculation errors and that our answer makes logical sense in the context of the problem.

Final Answer

After all our calculations and verifications, we've arrived at the final answer. We started with a word problem, translated it into a mathematical equation, solved for the unknowns, and then verified our solution. It’s been quite the journey, guys! The question we set out to answer was: How old is Alina?

We determined that Mihai is 19 years old and Alina is 76 years old. Therefore, the final answer is that Alina is 76 years old.

So, there you have it! We’ve successfully solved this age-related math problem. Remember, the key to tackling these kinds of problems is to break them down into smaller, manageable parts. Understand the information given, set up an equation, solve for the unknowns, and always verify your solution. Math can be like a fun puzzle if you approach it step by step. Great job, everyone!