Unlocking Math: Equations & Cost Analysis

Hey guys! Let's dive into some cool math problems today. We're gonna tackle equations and even a bit of real-world finance stuff. Don't worry, it's not as scary as it sounds! We'll break everything down step-by-step to make sure you understand it completely. So, grab your pencils and let's get started. This is all about applying your math skills in practical situations, so pay close attention. It's like learning a superpower that helps you solve everyday puzzles. By the end of this, you will know how to easily solve the equations and use your knowledge to figure out the cost of things. This is a must-know skill that will benefit you in so many ways. Remember that math is not about memorizing formulas; it's about understanding the logic behind them. The goal is not just to get the right answer but also to understand why it's the right answer. Ready? Let's go!

(a) Solving Equations

Alright, let's kick things off with solving some equations. We'll look at two different scenarios and figure out how to find the unknown numbers. This is where you put on your detective hat and start looking for clues. The key to solving these types of problems is to translate the words into mathematical expressions. Once you have that, it's just a matter of using your algebra skills to isolate the variable. Let's break down the first equation together. We'll identify the key information and then make sure we clearly understand what it means. Remember, practice makes perfect. The more problems you solve, the better you will become at this. Don't worry if you get stuck, everyone does at some point. The most important thing is to keep trying and to learn from your mistakes. Embrace the challenge and have fun with it! So, let's explore these equations and see how we can unravel the mysteries hidden within them. Are you ready to crack the code? Let's get started, and let me know if you get stuck along the way.

α. Decoding the First Equation

Let's tackle the first equation, shall we? Ten added to thrice a whole number gives 40. What does this even mean? Well, let's break it down piece by piece. First, let's assign a variable to the unknown whole number. Let's call it 'x'. The term "thrice a whole number" means three times the number, so it becomes 3x or 3x. "Ten added to thrice a whole number" translates to 10 + 3x. Finally, "gives 40" means that the whole expression equals 40. Now, we have a complete equation: 10 + 3x = 40. Solving for x is simple. First, subtract 10 from both sides of the equation. This gives us 3x = 30. Now, divide both sides by 3, and you get x = 10. So, the whole number is 10. Let's analyze it and make sure it makes sense. If you multiply 10 by 3 you get 30. Then, adding 10 to 30 will give you 40, which matches the right side of the equation. Excellent! We've successfully solved our first equation. High five! Now we will see another type of equation. It's always a good idea to check your answer like this to make sure you have the right answer. We will continue this practice through the rest of the exercises to ensure you know the solution and are not just guessing. In this way, you can solidify your learning and improve your confidence. Are you ready for the next challenge? Let's jump in.

β. Cracking the Second Equation

Alright, let's move on to our second equation. Four-fifths of a number is greater than three-fourths of a number by 8. Okay, this one sounds a little trickier, but don't worry, we've got this. Again, let's start by assigning a variable to the unknown number. Let's stick with 'x'. "Four-fifths of a number" translates to (4/5)x. "Three-fourths of a number" translates to (3/4)x. "Is greater than...by 8" means that the difference between (4/5)x and (3/4)x is 8. So, the equation is: (4/5)x - (3/4)x = 8. Now we need to solve for x. The first step is to find a common denominator for the fractions. The least common denominator (LCD) of 5 and 4 is 20. So, we rewrite the fractions with the denominator of 20: (16/20)x - (15/20)x = 8. Now, subtract the fractions: (1/20)x = 8. To solve for x, multiply both sides of the equation by 20. This gives us x = 160. So, the number is 160. Let's double-check our answer. Four-fifths of 160 is 128. Three-fourths of 160 is 120. The difference between 128 and 120 is indeed 8. Awesome! We've solved the second equation successfully! Now you know how to solve some basic equations and will know how to solve them in the future. Remember to take things step by step and break down the problem. Let me know if you would like me to explain any part of this in more detail.

(b) Cost Analysis of Malt Drinks

Now, let's switch gears and dive into the world of finance. We're going to calculate the cost of a crate of malt drinks and how much each bottle costs. This is practical stuff that you will definitely use in real life! The main skill we will work on is the ability to use basic arithmetic to solve problems. This ability will help you in your daily life, and more importantly, it helps you in your professional life. Understanding how money works is crucial in today's world. Let's get started. Financial literacy is super important, guys! Knowing how to calculate costs and manage money can help you make smart choices and avoid unnecessary expenses. Are you ready to learn about the cost of a crate of malt drinks?

Calculating the Cost Per Bottle

A crate of malt drink costs GH$ 90.00. Okay, so we know the total cost of a crate. We are also told that the crate contains 30 bottles. The next step is to calculate the cost of each bottle. This is simple, right? To find the cost of each bottle, you will need to divide the total cost of the crate by the number of bottles in the crate. So, we'll divide GH$90.00 by 30 bottles. The calculation will be 90/30 = 3. Therefore, the cost of each bottle is GH$3.00. That's pretty straightforward, right? Imagine you're at the store and you are trying to make a budget. Knowing how to calculate the cost per unit helps you make an informed decision about whether you want to purchase a product. It's a key skill for smart shopping and will make you a more informed consumer. Now, let's put it all together. You have successfully figured out how to solve equations and how to solve a basic financial calculation. It is time to pat yourself on the back. It is okay to feel proud because you have come so far! Remember to keep practicing and learning. You're doing great! Keep up the amazing work.

Putting It All Together

So, there you have it, guys! We have solved two different types of equations, and we have figured out the cost per bottle of a malt drink. We've used different mathematical concepts to solve these problems, including simple algebra and division. We have proven that the knowledge is powerful and can be used to solve different types of problems. Isn't that cool? It's all about breaking down problems, understanding what's being asked, and using the right tools to find the answers. You guys have done a fantastic job today. Remember, practice is key. Keep working on these kinds of problems, and you'll become even more confident and skilled at solving them. If you have any questions or want to try some more problems, just let me know. You have proven that you can do it. Always believe in yourselves, and keep up the amazing work!