Eva And Rosa's Purses: Solving The Equation

Hey guys! Today, we're diving into a fun little math problem about Eva and Rosa making purses. It's a classic example of how we can use equations to solve real-world scenarios. So, grab your thinking caps, and let's get started!

Breaking Down the Problem

Okay, so the problem tells us that Eva and Rosa together make 120 purses. That's our total. We also know that Rosa makes 50 more purses than Eva. The big question is: how many purses does Eva make? To solve this, we need to translate this word problem into a mathematical equation. This is where the magic happens, and we turn words into symbols and numbers.

Keywords are super important here. They're like clues that help us unlock the solution. Phrases like "together make" tell us we're dealing with addition. "More than" also indicates addition, but in a slightly different way. It means we're adding something to Eva's total to get Rosa's total. Identifying these keywords is the first step in setting up our equation. We need to understand the relationships between the quantities before we can write them down mathematically.

Think of it like building a bridge. Each piece of information is a component, and the equation is the blueprint that connects them all. If we miss a piece or misinterpret it, our bridge (or equation) won't be stable. So, let's make sure we've got all the pieces in the right place. We'll start by assigning variables to the unknowns, which will be Eva's and Rosa's purse counts. Then, we'll express the given relationships using those variables and mathematical operations. Finally, we'll have a complete equation that we can solve for the answer.

Setting Up the Equation

Let's use a variable to represent the number of purses Eva makes. We'll call it "x". So, x equals the number of purses Eva makes. Now, since Rosa makes 50 more purses than Eva, we can represent the number of purses Rosa makes as "x + 50". This is because we're adding 50 to Eva's total to get Rosa's total. It's like saying if Eva makes 20 purses, Rosa makes 20 + 50 = 70 purses.

We also know that the total number of purses they make together is 120. This means Eva's purses (x) plus Rosa's purses (x + 50) equals 120. This gives us our equation:

x + (x + 50) = 120

This equation is the heart of the problem. It encapsulates all the information we've been given in a concise mathematical statement. The left side represents the combined number of purses made by Eva and Rosa, and the right side represents the total number of purses. The equal sign signifies that these two quantities are the same. Now, all that's left to do is solve this equation for x, which will tell us how many purses Eva made.

This step is crucial because it's where we transition from a word problem to a mathematical one. We've taken the given information and translated it into a symbolic representation. This is a fundamental skill in algebra and problem-solving in general. The ability to set up equations like this allows us to tackle a wide range of problems, from simple everyday calculations to complex scientific inquiries. So, let's move on to the next step and solve this equation to find our answer!

Solving for Eva's Purses

Now that we have our equation, x + (x + 50) = 120, let's solve for x. The first thing we need to do is simplify the equation. We can do this by combining like terms. On the left side, we have x + x, which equals 2x. So, our equation becomes:

2x + 50 = 120

Next, we want to isolate the term with x on one side of the equation. To do this, we need to get rid of the +50. We can do this by subtracting 50 from both sides of the equation. Remember, whatever we do to one side of the equation, we have to do to the other side to keep it balanced. So, we subtract 50 from both sides:

2x + 50 - 50 = 120 - 50

This simplifies to:

2x = 70

Now, we have 2x equals 70. To solve for x, we need to get x by itself. Since x is being multiplied by 2, we can undo this by dividing both sides of the equation by 2:

2x / 2 = 70 / 2

This gives us:

x = 35

So, we've found that x equals 35. Remember, x represents the number of purses Eva makes. Therefore, Eva makes 35 purses. This is our answer! We've successfully solved the equation and answered the question. But before we celebrate, let's make sure our answer makes sense in the context of the original problem.

Checking Our Answer

It's always a good idea to check our answer to make sure it's correct. We found that Eva makes 35 purses. The problem also told us that Rosa makes 50 more purses than Eva. So, Rosa makes 35 + 50 = 85 purses. Now, let's see if the total number of purses they make together is 120:

35 (Eva's purses) + 85 (Rosa's purses) = 120

It checks out! Our answer is consistent with the information given in the problem. Eva makes 35 purses, Rosa makes 85 purses, and together they make 120 purses. This confirms that our solution is correct.

Checking our work is a crucial step in problem-solving. It helps us catch any mistakes we might have made and ensures that our answer is reasonable. It's like proofreading a document before submitting it – it's a final check to make sure everything is perfect.

Expressing the Solution

So, the final answer is: Eva makes 35 purses. We've not only solved the equation but also interpreted the solution in the context of the problem. It's important to remember that in word problems, the answer should always be expressed in a way that answers the original question. In this case, the question was "How many purses does Eva make?", so our answer should be "Eva makes 35 purses."

This step highlights the importance of understanding the question being asked and providing a clear and concise answer. It's not enough to just find a numerical value; we need to connect that value back to the real-world scenario described in the problem. This is what makes mathematical problem-solving relevant and meaningful. We're not just manipulating numbers; we're using math to understand and solve problems in the world around us.

Conclusion

And there you have it! We've successfully solved the problem of Eva and Rosa's purses. We broke down the problem, set up an equation, solved for the unknown, and checked our answer. This is the process of mathematical problem-solving in action. Remember, the key is to understand the problem, identify the relationships between the quantities, translate those relationships into an equation, and then solve the equation. Keep practicing, and you'll become a pro at solving these types of problems!

If you guys have any questions or want to try another problem, let me know in the comments below. Happy problem-solving!