Teresa And Carmen's Market Trip: A Math Problem Solved!

Hey guys! Today, we're diving into a fun math problem about Teresa and Carmen's trip to the market. Let's break it down step by step and make sure we understand everything clearly. So, grab your thinking caps, and let's get started!

Understanding the Problem

First things first, let’s recap the situation. Teresa is buying 6 kg of meat, and Carmen is buying 2 kg. The price of each kilogram of meat is 9 nuevos soles. Our mission is to figure out how much they spent in total. This is a classic example of a problem that combines addition and multiplication, which are fundamental concepts in mathematics. To solve this problem effectively, we need to identify the key steps and apply the correct operations.

Breaking Down the Information

To make things easier, let’s list out the known information:

• Teresa's meat: 6 kg
• Carmen's meat: 2 kg
• Price per kg: 9 nuevos soles

By clearly identifying these pieces of information, we set the stage for an organized solution. This is a great strategy for tackling any word problem in math. Now that we have all the facts laid out, we can start to formulate our approach. Think of it like gathering all the ingredients before you start cooking – it makes the whole process smoother and more efficient.

Formulating the Solution

The first thing we need to figure out is the total amount of meat that Teresa and Carmen bought together. We can find this by adding the amount Teresa bought to the amount Carmen bought:

$6 \text{ kg} + 2 \text{ kg} = 8 \text{ kg}$

So, together they bought 8 kg of meat. Now that we know the total amount of meat, we can calculate the total cost by multiplying the total weight by the price per kilogram:

$8 \text{ kg} \times 9 \text{ nuevos soles/kg} = 72 \text{ nuevos soles}$

Therefore, Teresa and Carmen spent a total of 72 nuevos soles. This is a clear and straightforward solution. The key was to break the problem into smaller, manageable steps. Always remember, in math, breaking down complex problems into simpler parts is a powerful technique!

Solving the Equation

Now, let's tackle the equation part of the problem. We need to complete the following equation:

$7 \times (\Box + \Box) = (\Box \times \Box) + (\Box \times \Box)$

This equation is based on the distributive property of multiplication over addition. The distributive property states that for any numbers a, b, and c:

$a \times (b + c) = (a \times b) + (a \times c)$

In our case, we need to find suitable numbers to fill in the boxes so that the equation holds true.

Applying the Distributive Property

Let's choose two numbers, say 3 and 4, to put inside the parentheses. Then the equation becomes:

$7 \times (3 + 4) = (7 \times 3) + (7 \times 4)$

Now, let's solve each side of the equation to see if it balances:

Left side:

$7 \times (3 + 4) = 7 \times 7 = 49$

Right side:

$(7 \times 3) + (7 \times 4) = 21 + 28 = 49$

Since both sides of the equation equal 49, our equation is correct! Therefore, the completed equation is:

$7 \times (3 + 4) = (7 \times 3) + (7 \times 4)$

Generalizing the Solution

It's important to note that we could have chosen any two numbers for the boxes, and the equation would still hold true as long as we followed the distributive property correctly. For example, let’s try 1 and 5:

$7 \times (1 + 5) = (7 \times 1) + (7 \times 5)$

Left side:

$7 \times (1 + 5) = 7 \times 6 = 42$

Right side:

$(7 \times 1) + (7 \times 5) = 7 + 35 = 42$

Again, both sides equal 42, so the equation is valid. This demonstrates the flexibility and power of the distributive property.

Importance of Understanding the Distributive Property

The distributive property is a fundamental concept in algebra and is used extensively in various mathematical operations. Understanding this property helps in simplifying complex expressions and solving equations. In real-world scenarios, it can be applied in situations such as calculating costs, dividing resources, and many other practical applications. Think of it as a versatile tool in your math toolkit!

Practical Applications

Let's consider a practical example. Suppose you are buying 7 sets of items, and each set contains 3 apples and 4 oranges. The total number of fruits can be calculated using the distributive property:

$7 \times (3 \text{ apples} + 4 \text{ oranges}) = (7 \times 3) \text{ apples} + (7 \times 4) \text{ oranges} = 21 \text{ apples} + 28 \text{ oranges}$

This shows how the distributive property can be used to simplify calculations in everyday situations. It's not just an abstract mathematical concept; it has real-world relevance.

Conclusion

So, there you have it! We've successfully solved the problem about Teresa and Carmen's market trip, and we've also completed the equation using the distributive property. Remember, breaking down problems into smaller steps and understanding the underlying mathematical principles are key to success in math. Keep practicing, and you'll become a math whiz in no time! And always remember, math isn't just about numbers; it's about problem-solving and critical thinking. Keep those brains sharp, guys!