Sales Target: How Much Must Maria Sell To Earn $4800?

Understanding the Commission Structure

Hey guys! Let's dive into this math problem where Maria earns a commission of 12% on her sales. The big question is: how much does she need to sell to make $4800? This is a classic percentage problem, and we're going to break it down step by step so it's super easy to understand. First, it's crucial to understand what a percentage actually represents. In this case, 12% means that for every $100 worth of sales Maria makes, she earns $12. This is her commission rate. To figure out the total sales needed, we need to find out what amount, when multiplied by 12%, gives us $4800. You might be thinking, "Okay, but how do we actually do that?" Don't worry, we've got you covered. We're essentially working backwards here. Instead of calculating the commission from the sales, we're calculating the sales from the desired commission. This involves using a little bit of algebra, but trust me, it's nothing scary. Think of the total sales amount as our mystery variable, let's call it 'x'. We know that 12% of 'x' equals $4800. So, we can write this as an equation: 0. 12 * x = 4800. See? It looks much less intimidating when it's written down. Now, to solve for 'x', we need to isolate it on one side of the equation. This means we need to get rid of that 0.12 that's hanging out next to it. We do this by dividing both sides of the equation by 0.12. Remember, whatever we do to one side of the equation, we have to do to the other to keep things balanced. This is a fundamental rule of algebra. So, when we divide both sides by 0.12, we get: x = 4800 / 0.12. Now it's just a matter of doing the math. You can use a calculator for this, or if you're feeling brave, you can do it by hand. Either way, the answer will give us the total sales amount Maria needs to achieve her $4800 goal. So, grab your calculators, or your thinking caps, and let's get to solving!

Setting Up the Equation

Okay, so we know that Maria's commission is 12% of her total sales, and she wants to earn $4800. Let's translate this into a mathematical equation. This is a crucial step because it allows us to use the power of algebra to solve the problem. We need to represent the unknown total sales with a variable. Let's use 'x' – it's a classic choice! Now, how do we express 12% as a number we can use in an equation? Percentages are just fractions out of 100, so 12% is the same as 12/100. To make it a decimal, we simply divide 12 by 100, which gives us 0.12. Remember this conversion; it's super important for working with percentages. So, 12% is mathematically represented as 0.12. Now we can build our equation. We know that 12% (or 0.12) of the total sales (x) equals $4800. In mathematical terms, "of" often means multiplication. So, we can write our equation as: 0.12 * x = 4800. This equation is the heart of our problem. It tells us that 0. 12 multiplied by the total sales (x) will give us Maria's desired earnings of $4800. This is a linear equation, and solving it will give us the value of 'x', which is the total sales amount Maria needs. To make sure we're on the right track, let's think about what this equation means in plain English. It's saying that if we take 12% of Maria's total sales, we should get $4800. If the number we get for 'x' doesn't seem reasonable in this context, then we know we might have made a mistake somewhere. So, always take a moment to check if your answer makes sense in the real world. This is a great way to catch errors. Now that we have our equation set up, the next step is to solve it. This involves isolating 'x' on one side of the equation, which we'll tackle in the next section.

Solving for Total Sales

Alright guys, we've got our equation: 0.12 * x = 4800. Now it's time to solve for 'x', which represents the total sales Maria needs to make. Solving for a variable in an equation is like unlocking a puzzle. Our goal is to get 'x' all by itself on one side of the equation. Right now, 'x' is being multiplied by 0.12. To undo this multiplication, we need to perform the opposite operation, which is division. Remember, whatever we do to one side of the equation, we have to do to the other side to keep it balanced. So, we're going to divide both sides of the equation by 0.12. This will cancel out the 0.12 on the left side, leaving 'x' by itself. Let's write it down: (0.12 * x) / 0.12 = 4800 / 0.12. On the left side, the 0.12 in the numerator and the denominator cancel each other out, leaving us with just 'x'. So, we now have: x = 4800 / 0.12. Now it's just a matter of performing the division. You can use a calculator for this, or you can do it manually if you're feeling confident. Either way, the result will give us the value of 'x', which is the total sales Maria needs. When you divide 4800 by 0.12, you get 40000. So, x = 40000. This means Maria needs to make $40,000 in sales to earn $4800 in commission. It's always a good idea to double-check your answer to make sure it makes sense. We can do this by plugging the value of 'x' back into our original equation. So, let's calculate 0.12 * 40000. This gives us 4800, which is exactly the amount Maria wants to earn. So, our answer checks out! We've successfully solved for 'x' and found the total sales amount. Now, let's move on to the final step, which is to interpret our answer in the context of the problem.

Interpreting the Result and Final Answer

Okay, we've done the math and found that x = 40000. But what does this mean in the real world? It's super important to understand what our answer represents in the context of the problem. Remember, 'x' represents the total amount of sales Maria needs to make. So, x = 40000 means Maria needs to sell $40,000 worth of products to earn her desired commission of $4800. That's a pretty significant amount! It gives us a good sense of the scale of sales Maria needs to achieve. Now, let's go back to the original question. It asked: "How much will María have to sell to earn $4800?" We've just figured out that the answer is $40,000. So, Maria needs to sell $40,000 worth of products. Let's check this against the answer choices provided. The options were: a. $40,000 b. $520,000 c. $60,000 d. $48,000. Our calculated answer of $40,000 matches option (a). So, the final answer is (a) $40,000. We've not only found the answer, but we've also understood what it means in the context of the problem. This is a crucial skill in math and problem-solving. It's not just about getting the right number; it's about understanding what that number represents. So, to recap, we set up an equation, solved for the unknown variable, and then interpreted the result. This is a common approach to solving many word problems. We can confidently say that Maria needs to sell $40,000 worth of products to earn $4800 in commission. We've successfully tackled this percentage problem!

Key Takeaways for Solving Percentage Problems

Alright, we've successfully solved this problem about Maria's sales goals. But let's take a step back and think about the key takeaways that can help you tackle similar percentage problems in the future. Understanding the underlying principles is way more valuable than just memorizing steps. First, always make sure you understand what the percentage represents. In this case, 12% means $12 earned for every $100 in sales. Knowing this fundamental concept is crucial for setting up the problem correctly. Second, translating word problems into mathematical equations is a key skill. Look for keywords like "of," which often indicates multiplication, and phrases like "is equal to," which translates to the equals sign (=). Breaking down the problem into smaller parts and then expressing it mathematically makes it much easier to solve. Third, when dealing with percentages, remember to convert them to decimals before using them in equations. To do this, divide the percentage by 100. So, 12% becomes 0.12. This conversion is essential for accurate calculations. Fourth, setting up the equation correctly is half the battle. In our case, we knew that 12% of the total sales equals $4800. So, we wrote the equation as 0.12 * x = 4800. Make sure the equation accurately reflects the information given in the problem. Fifth, solving for the unknown variable involves isolating it on one side of the equation. Remember to perform the same operations on both sides to maintain balance. In this case, we divided both sides by 0.12 to isolate 'x'. Sixth, once you've found the answer, always double-check it by plugging it back into the original equation. This helps you catch any errors and ensures that your solution is correct. Finally, interpret the result in the context of the problem. Don't just focus on the number; understand what it represents in the real world. In our case, $40,000 represents the total sales Maria needs to make. By keeping these takeaways in mind, you'll be well-equipped to solve a wide range of percentage problems. So, keep practicing, and you'll become a percentage pro in no time!