Рост Алишера И Самандарда: Алгебраическое Разложение

Hey guys! Let's dive into a fun algebra problem involving the heights of Alisher and Samandar. We're given some cool information and need to figure out a few things. So, get ready to flex those math muscles!

a) Отношение роста Алишера и Самандарда

Okay, so first things first: we need to find the relationship between Alisher's height and Samandar's. We already know some key facts. The problem tells us that Alisher's height is $\frac{7}{6}$ of Samandar's height. This is super helpful! Basically, Alisher is a bit taller, and we know exactly how much taller. To express this relationship, we need to compare their heights. The ratio will show us how many times bigger Alisher's height is relative to Samandar's. Let's break this down further! Since Alisher’s height is $\frac{7}{6}$ of Samandar's, the ratio of Alisher's height to Samandar's height is simply $\frac{7}{6}$. So the ratio of Alisher's height to Samandar's height can be expressed as 7:6. This means for every 7 units Alisher grows, Samandar grows 6. It's like a direct comparison, easy peasy, right? The question is straightforward, and the answer directly comes from the problem statement itself, making this part a breeze. Now we know the ratio of Alisher's height to Samandar's height is $\frac{7}{6}$ or 7:6. We just found it and this answers the first part of our question. Now on to the next part where we're going to find out how tall Samandar is.

Here’s how we can represent this mathematically and in a way that's easy to grasp. We can write this as:

• Alisher's height : Samandar's height = 7 : 6

This simple ratio tells us everything we need to know about the proportional relationship between their heights. The ratio directly gives us the proportional comparison, and we can move on to other calculations with that piece of information. This is very important when tackling the next question.

Now, let's look at the implications of this ratio. If we knew Samandar's height, we could find Alisher's by multiplying it by $\frac{7}{6}$. If we knew Alisher's height, we could find Samandar's by multiplying by $\frac{6}{7}$. The ratio helps in understanding their heights relative to each other. This kind of problem is fundamental to algebra, introducing concepts like proportions and ratios. These are foundational principles that you'll use over and over again in more complex mathematical problems. Keep in mind that understanding ratios makes solving all kinds of problems easier, especially those that involve comparisons of quantities.

So, to recap the first part. The ratio of Alisher's height to Samandar's height is 7:6 or $\frac{7}{6}$. This answers the first part of the problem. Simple, right?

b) Рост Самандарда

Alright, let’s find out how tall Samandar is! We know Alisher is 140 cm tall, and we also know that Alisher's height is $\frac{7}{6}$ of Samandar's height. Think about this for a second. We can set up an equation to find Samandar's height. Let's call Samandar's height 'x'. The equation will be: $\frac{7}{6} * x = 140$. Now, we need to solve for 'x'. To do this, we'll multiply both sides of the equation by $\frac{6}{7}$. Doing this will isolate 'x' on one side, giving us Samandar's height. Let’s do it step by step so it's clear for everyone. First, we write the equation: $\frac{7}{6}x = 140$. Next, we multiply both sides by $\frac{6}{7}$: $(\frac{6}{7}) * (\frac{7}{6})x = 140 * (\frac{6}{7})$. This simplifies to: $x = (140 * 6) / 7$. Then we calculate: $x = 840 / 7$. Finally, we divide: $x = 120$ cm. So, Samandar is 120 cm tall! It's like a math detective game where we use the clues to find the unknown value. The calculation involves solving a simple algebraic equation that is a fundamental concept in mathematics.

So, Samandar's height is 120 cm. We found this by using the ratio and the known height of Alisher. This also demonstrates the practical application of solving equations with fractions. You might encounter similar problems in everyday situations. For example, if you are scaling a recipe, you are essentially working with proportions and equations. Keep in mind that this kind of problem is common in many different contexts. If you want to double a recipe, you are dealing with a proportion. Therefore, understanding these fundamental principles can be applied universally, far beyond a simple algebra problem.

By understanding how to solve this problem, you gain a foundational understanding of the relationship between ratios, fractions, and proportions, all of which are critical for future math studies and real-world applications. These skills are essential, and the more practice you get, the easier they become. If you want to increase your math skills, try similar problems with different numbers. This helps solidify your understanding of these principles, and it also boosts your confidence.

Let’s summarize the solution! We determined the ratio of Alisher's height to Samandar's height and calculated Samandar's height. We did this by setting up an equation and solving for the unknown variable. Keep practicing; the more you practice, the better you get!