Meal Prices: Calculate Paula's Traditional And Fitness Meal Costs

Hey guys! Let's dive into a fun math problem! We're going to figure out the price of two types of meals that Paula sells: traditional and fitness. Here's the deal: Paula sold 10 traditional meals and 5 fitness meals, and she made a total of R$175.00. Our mission? To calculate the price of each type of meal. We'll use a little algebra to crack this. Get ready to put on your thinking caps! First off, let's break down the problem to its core components. We know the total amount earned, the number of each type of meal sold, and that the prices are different. What we don't know, are the individual prices! Let's denote the price of the traditional meal as 'X' and the price of the fitness meal as 'Y'. The goal is to use the information to build an equation to find X and Y. Sounds fun, right? Understanding the basics is key. In this case, the basics revolve around setting up an algebraic equation that mirrors the information provided in the problem. Since the total revenue is given, we can use it to build the equation. This helps us get a grip on the prices. It makes the whole process much simpler. Plus, once we set up this equation, we can solve for the unknown variables, finding the price. So, how can we turn the data into an equation?

Well, we know that Paula sold 10 traditional meals at a price of X each, and 5 fitness meals at a price of Y each. The total revenue is equal to the earnings from both types of meals. So, the equation should be built around that relationship. It will connect the prices, number of meals, and total revenue. As you learn more about how to approach these kinds of math problems, you'll soon be creating complex equations in your head! The key takeaway from this initial phase is to understand what the problem asks and what data is available, the starting point for forming our equations.

Formulating the Equation

Alright, let's get to the heart of the matter! We're building our equation to figure out those meal prices. Remember, 'X' is the price of a traditional meal, and 'Y' is the price of a fitness meal. Paula sold 10 traditional meals, so the total earnings from those meals are 10X. She also sold 5 fitness meals, which amounts to 5Y. We know the total revenue from both types is R$175.00. Therefore, to get our equation, all we have to do is add the earnings from the traditional meals (10X) and the earnings from the fitness meals (5Y), and set the sum equal to the total revenue of R$175.00. The equation we're going to use to solve this problem is: 10X + 5Y = 175. That's it! Simple, right? This equation represents the relationship between the number of meals sold, their prices, and the total amount of money earned. It's a fantastic starting point that we need to find the individual meal prices. If we had another equation we could solve this, but we don't. Let's see how this could work with another known figure.

Imagine that you also know that a traditional meal is R$5.00 more expensive than a fitness meal. Now the equation gets much easier. We can modify our original equation. Now X is Y + 5. To make this equation work we will change X. The new equation would be 10(Y+5) + 5Y = 175. We can then solve for Y. Once you have found Y, you will also have the price for X. Another approach could be that the prices are related by a percentage. So the traditional meal is 10% more expensive than the fitness meal. The world of math has many ways to solve problems. For this specific case we can not solve the equation as we have it, we can only express it in this form. If you want to give it a try, you can change some numbers and apply some of these methods to try to solve the equation.

Solving the Equation (If we had enough information!)

Unfortunately, with just one equation (10X + 5Y = 175), we can't pinpoint the exact values of X and Y. That's because we need at least two independent equations to solve for two unknowns. Think of it like this: each equation represents a line on a graph, and the solution is where the lines intersect. So, in our problem, we'd need another piece of information, such as the price of a traditional meal relative to a fitness meal or the price of one of the meals. For example, if we knew that a traditional meal (X) cost R$10.00, we could substitute that value into our equation. Our modified equation would be 10(10) + 5Y = 175, which we can solve for Y. That means the price of fitness meal is Y. Let's go with this assumption. 100 + 5Y = 175. Now we just have to get Y alone on the left side, so we remove 100 from both sides: 5Y = 75. Now divide each side by 5 and you get Y = 15. Now, if we know X (10) and Y (15) then our solution is that the fitness meal is more expensive than the traditional meal. We got it wrong, but the method is correct! With more information, we can solve it!

Conclusion: Setting up the Equation and Why It Matters

So, guys, we've successfully set up the equation: 10X + 5Y = 175. This equation captures the relationship between the number of meals sold, their prices, and the total revenue. While we couldn't solve for specific values of X and Y with just one equation, the process of formulating the equation is incredibly valuable. It demonstrates how we can translate a word problem into a mathematical expression. Think of this as the first step to cracking more complex problems. Even though we didn't get to a concrete answer this time, the skills we've practiced are useful in all aspects of life. We've learned how to analyze a problem, identify key information, and represent it in a mathematical form. This process helps us think critically and solve real-world problems. Remember, it's not always about the final answer; it's about the process, the understanding, and the learning. So, next time you face a math problem, remember our equation and remember how we broke it down step-by-step. Thanks for joining me on this math adventure! Until next time, keep practicing and keep those brains working!