Shirt Purchase Problem: How To Find 'e'?

Hey guys! Let's dive into this interesting math problem about Pedro buying a bunch of shirts. We'll break it down step by step so it's super easy to understand. This isn't just about numbers; it's about understanding how math applies to real-life situations, like buying and selling stuff. So, grab your thinking caps, and let's get started!

Understanding the Problem

So, the core of the problem revolves around Pedro's shirt purchase. He's buying these shirts in bulk – we're talking thousands! And the price is given per thousand shirts. It's like buying in wholesale, where you get a better deal when you buy more. The tricky part here is figuring out what 'e' represents and how we can find it by solving the system related to this purchase. We need to really dig into the details to understand all the pieces of the puzzle. What does 'e' stand for? Is it the total cost, the number of shirts, or something else entirely? Once we nail down what we're looking for, the rest should fall into place more easily.

Key Information

• Quantity: Pedro buys shirts in thousands.
• Price: The price is 5 soles per thousand shirts.
• The Unknown: We need to figure out what 'e' represents and how to calculate it.

Breaking Down the Tricky Part: What is 'e'?

Okay, let's talk about this mysterious 'e'. In math problems, letters often stand for unknown values or variables. So, 'e' could represent a bunch of different things related to Pedro's shirt purchase. It could be:

1. The total number of shirts Pedro bought. Maybe he bought 3000 shirts, so 'e' would be 3.
2. The total cost of the shirts. This would depend on how many thousands of shirts he bought.
3. Some other calculation related to the purchase, like the profit margin if he were to resell the shirts.

To really crack this, we need more context. Is there an equation or system of equations that uses 'e'? Are there any other clues in the original problem statement that might tell us what 'e' is all about? Let's keep digging!

Setting Up the Equations

Alright, let's move on to the next crucial step: setting up the equations. Math problems like this often need an equation (or a system of equations) to solve them. Think of equations as the secret code to unlock the answer. They show the relationship between different values. In our case, we need to connect the number of shirts, the price per thousand, and, of course, our unknown 'e'. This is where we start translating the words of the problem into mathematical language. We'll use symbols and numbers to represent the information we already have, and then we'll create equations that show how those pieces fit together.

Defining Variables

First, we need to define our variables. This is like giving names to the different things we're working with. It helps us keep track of everything and makes the equations easier to write. Let's use:

• x: to represent the number of thousands of shirts Pedro buys.
• C: to represent the total cost of the shirts in soles.

Building the Equation

Now we can build an equation to represent the total cost. We know that each thousand shirts costs 5 soles. So, if Pedro buys x thousands of shirts, the total cost C would be:

C = 5 * x

This simple equation is a powerful tool! It tells us exactly how the total cost changes depending on how many thousands of shirts Pedro buys. If Pedro buys one thousand shirts (x = 1), the cost is 5 soles. If he buys two thousand (x = 2), the cost is 10 soles, and so on. But remember, we're still trying to figure out what 'e' is. This equation might be part of a larger system, and 'e' might be related to C or x in some way.

The System of Equations

The problem mentions a "system" of equations, which means there's likely more than one equation involved. This makes things a bit more complex, but also more interesting! A system of equations is like a puzzle where you have multiple pieces that need to fit together perfectly. To solve for 'e', we'll probably need to use all the equations in the system. We need to look for more information in the problem statement or any clues that might suggest another equation. Perhaps there's information about Pedro's budget, or how many shirts he plans to sell, or some other factor that would give us another equation to work with. Once we have the complete system, we can use different methods (like substitution or elimination) to solve for the unknowns, including our mysterious 'e'.

Solving for 'e'

Okay, guys, here's where the real fun begins! We've laid the groundwork by understanding the problem and setting up the equations. Now, we're ready to solve for 'e'. This is like the detective work of math, where we use our knowledge and skills to uncover the hidden value. The exact steps we take will depend on the system of equations we have. There are a few common methods we can use, and we'll explore them in detail. But the key thing to remember is that solving for 'e' is like following a logical path. Each step leads us closer to the solution, and with careful work, we'll get there!

Methods to Solve Equations

Let's quickly recap some of the most common methods for solving equations. These are our go-to tools when we're faced with a system of equations:

• Substitution: This method involves solving one equation for one variable and then substituting that expression into another equation. It's like replacing a piece in a puzzle with its equivalent. This helps us reduce the number of variables and simplify the problem.
• Elimination: Elimination is all about adding or subtracting equations to get rid of one variable. It's like strategically canceling out terms to make the equations easier to solve. This often involves multiplying one or both equations by a constant to make the coefficients of one variable match.
• Graphing: Sometimes, we can solve a system of equations by graphing them and finding the point where they intersect. This works well for linear equations, where the graphs are straight lines. The intersection point represents the values of the variables that satisfy both equations.

Applying the Methods

To actually solve for 'e', we need to see the full system of equations. Let's imagine we have a second equation that relates 'e' to the number of thousands of shirts x and the total cost C. For example, maybe 'e' represents the profit Pedro makes if he sells the shirts at a certain price. In that case, we might have an equation like:

`e = (Selling Price per Shirt - Cost per Shirt) * Total Number of Shirts`

If we had specific numbers for the selling price and the number of shirts, we could plug them into this equation along with the equation C = 5 * x to solve for 'e'.

Let's say, for the sake of example, that we have the following system of equations:

1. C = 5x
2. e = 2x - C

We can use substitution to solve for 'e'. Since we know C = 5x, we can substitute that into the second equation:

`e = 2x - (5x)`
`e = -3x`

Now, to find a specific value for 'e', we'd need to know the value of x (the number of thousands of shirts). If Pedro bought 3000 shirts (x = 3), then:

`e = -3 * 3`
`e = -9`

In this example, 'e' would be -9. Remember, this is just an example to show how the solving process works. The actual system of equations and the meaning of 'e' might be different in the real problem.

Conclusion

So, guys, we've taken a deep dive into Pedro's shirt-buying adventure! We started by understanding the problem, then we set up equations to represent the situation, and finally, we explored how to solve for the mysterious 'e'. Remember, the key to solving these kinds of problems is to break them down into smaller, manageable steps. Identify the key information, define your variables, and build equations that show the relationships between those variables. And don't be afraid to experiment with different solving methods until you find one that works for you. Math is like a puzzle, and every problem is a chance to sharpen your skills and have some fun! Keep practicing, and you'll become a math whiz in no time!