Question

Познач найменшу з невідомих величин х і побудуй математичну модель задачі. Знайди х і дай відповіді на поставлені запитання. Задача: Краватка у 2 рази дешевша за сорочку а сорочка у 8 разів дешевша за костюм. Скільки коштує краватка якщо костюм коштує 1280 грн? СРОЧНО!! 30 балов

Answer 1

Problem Analysis

To solve this problem, we need to find the cost of the tie (kravatka) given that the suit (kostyum) costs 1280 UAH (Ukrainian Hryvnia). We are given that the tie is twice as cheap as the shirt (sorochka), and the shirt is eight times cheaper than the suit. We can represent the cost of the shirt as x, and then use this information to create a mathematical model of the problem.

Mathematical Model

Let's denote the cost of the shirt as x. According to the problem statement, the tie is twice as cheap as the shirt, so its cost can be represented as 2x. Similarly, the suit is eight times more expensive than the shirt, so its cost can be represented as 8x.

We are given that the suit costs 1280 UAH, so we can set up the following equation:

8x = 1280

To find the cost of the tie, we can substitute the value of x into the expression for the tie's cost:

2x

Solution

To solve the equation 8x = 1280, we can divide both sides of the equation by 8:

8x / 8 = 1280 / 8

This simplifies to:

x = 160

Now that we have the value of x, we can substitute it into the expression for the tie's cost:

2x = 2 * 160 = 320

Therefore, the tie (kravatka) costs 320 UAH.

Answer

The tie (kravatka) costs 320 UAH if the suit (kostyum) costs 1280 UAH.

I hope this helps! Let me know if you have any further questions.