Scale Drawing Problem: Calculate The Actual Feet

Hey everyone! Today, we're diving into a classic scale drawing problem. It's super important in real life – think architects, mapmakers, and even people planning their gardens! The core idea? We use a scaled-down version (the drawing) to represent something much larger in the real world. Let's break down this problem, and I promise, it's easier than it looks! So, let's get started on figuring out what 3/4 inch represents in terms of feet, given that 5 inches on our scale drawing equals 80 feet in reality. We'll be using the concept of proportions, which are just two ratios that are equal to each other. It's like saying, "If this, then that, at the same rate." The key here is to set up our ratios correctly to solve for the unknown value. Keep in mind that understanding scale drawings is not just about getting the right answer in a math problem; it's about developing a valuable skill that has tons of real-world applications. If you're planning a home renovation, understanding scale drawings helps you visualize the changes, estimate costs, and avoid potential problems down the line. Let's make sure we understand the question first, then we'll walk through the process, step by step, making sure every concept is super clear. Are you ready? Let's do it!

Understanding the Problem: Scale Drawings and Proportions

Okay, before we start crunching numbers, let's get a handle on what a scale drawing actually is. Imagine you're an architect designing a skyscraper. You can't exactly build a life-size model on your desk, right? That's where scale drawings come in! It's a way to represent a larger object or space on a smaller piece of paper while maintaining the correct proportions. The scale tells you how the measurements in the drawing relate to the actual measurements of the real-world object. In our case, the scale is pretty straightforward: 5 inches on the drawing equals 80 feet in reality. We want to find out how many feet are represented by 3/4 of an inch on the drawing. This kind of problem often appears in standardized tests, and it's super common in real-world situations, too. You'll find yourself needing this skill for everything, from reading maps to planning a room layout.

So, what does it mean to work with proportions? Essentially, a proportion is a statement that two ratios are equal. A ratio, in turn, is a comparison of two quantities using division. In our case, we'll set up a ratio of inches to feet. The ratio we know is: 5 inches / 80 feet. We also have another ratio with the 3/4 inch and an unknown number of feet, which we'll call x: (3/4) inches / x feet. Since the ratios are equal, we can set up an equation, and then solve for x. The cool thing is once you get the hang of it, solving these problems becomes a breeze. Now, let's work through this problem step-by-step to learn how to solve them so you can handle similar scenarios like a pro. Remember, the core concept is the proportional relationship between the drawing's measurements and the real-world measurements.

Step-by-Step Solution: Calculating the Unknown

Alright, guys, let's get down to the nitty-gritty and solve this problem step-by-step. First, let's restate what we know and what we need to find out. We're given that 5 inches on the scale drawing is equivalent to 80 feet in the real world. Our goal is to figure out how many feet are represented by 3/4 inch on the drawing. The most effective method here is to use proportions. We'll set up a proportion comparing inches to feet, making sure to keep the units consistent on both sides of the equation. First, we know that 5 inches corresponds to 80 feet. We can express this as a ratio: 5 inches / 80 feet. Then, we are told that 3/4 inch corresponds to an unknown number of feet which we'll call x. We can express this as a ratio: (3/4) inches / x feet. Because the ratios must be equal, we can set up the proportion: 5 inches / 80 feet = (3/4) inches / x feet.

Next, to solve for x, we'll use cross-multiplication. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction. This will give us: 5 * x = 80 * (3/4). Now we can simplify the right side of the equation. We know that 80 multiplied by 3/4 is the same as (80/4) * 3 which equals 20 * 3 = 60. So our equation now is: 5 * x = 60. To isolate x and solve for it, we will divide both sides of the equation by 5. That gives us: x = 60 / 5, which gives us x = 12. Therefore, 3/4 inch on the scale drawing represents 12 feet in the real world. See? It wasn't that hard, right? The key is setting up your ratios correctly, then using cross-multiplication. Practice a few more of these, and you'll be a pro in no time! So, now we know the answer.

The Answer and What It Means

So, after all that calculation, what's the answer? Drumroll, please… The correct answer is C. 12 feet! That means if 5 inches on the scale drawing represents 80 feet in reality, then 3/4 inch on that same drawing represents 12 feet. Now, let's think about this for a sec. Why is this important? Well, imagine you are an architect and you've drawn a small model of a building. To plan everything out in reality, the scale is necessary. What if you're trying to figure out how much material you need to build the building? You will use that scale to figure out how much space everything will take up. This math is fundamental for construction, design, and even everyday planning. This skill is critical for so many different fields, from engineering to interior design.

What did we learn? We learned how to use proportions to solve scale drawing problems. We learned to set up ratios correctly and solve for the unknown value. We converted units when necessary and applied cross-multiplication to solve the problem. More importantly, we learned that math isn’t just about memorizing formulas; it's about understanding how the world around us works. Whether you're planning a home renovation, designing a building, or just trying to figure out if that new couch will fit in your living room, understanding scale drawings and proportions can be an extremely useful and practical skill. So the next time you encounter a scale drawing, don’t be intimidated. Remember the steps we took, and you'll be able to solve these problems confidently. And there you have it, folks! This is the end of this problem, and I hope you found it helpful and enjoyable. Keep practicing, and you'll become a master of scale drawings in no time! If you have any more questions, feel free to ask!