Question

№1  В двух танкерах одинаковое количество нефти. Если из одного танкера перелить в другой 29 т, то нефти в 1-ом танкере останется в 2 раза меньше, чем станет во 2-ом. Сколько всего невти в обоих танкерах? №2 Сергей купил ручку, книгу, тетрадь и набор для черчения. Оказалось, что ручка на 6 р., а книга в 6 раз дороже тетради.Определите, какова стоймость каждого предмета, если известно, что набор в 4 раза дороже ручки и его стоймость равна стоймости книги.   Задачи для 6 класса. P.S Добавил бы больше пунктов если бы нои были =(

Answer 1

Task 1: Calculating the Total Amount of Oil in the Tankers

To solve this problem, let's assign variables to the quantities of oil in the tankers. Let's call the amount of oil in the first tanker "x" and the amount of oil in the second tanker "y".

According to the problem, if 29 tons of oil are transferred from the first tanker to the second tanker, the amount of oil in the first tanker will be half of what remains in the second tanker.

Mathematically, we can express this relationship as:

x - 29 = (y - 29) / 2

Simplifying the equation, we get:

2x - 58 = y - 29

Rearranging the equation, we have:

2x = y + 29 - 58

2x = y - 29

Now, let's solve the equation to find the relationship between x and y.

2x = y - 29

From the given information, we know that the initial amount of oil in both tankers is the same. Therefore, we can assume that x = y.

Substituting y with x in the equation, we get:

2x = x - 29

Simplifying the equation, we have:

x = -29

Since the amount of oil cannot be negative, this means that there is no solution to this problem. Therefore, we cannot determine the total amount of oil in both tankers based on the given information.

Task 2: Determining the Cost of Each Item

Let's assign variables to the cost of each item. Let's call the cost of the pen "p", the cost of the book "b", the cost of the notebook "n", and the cost of the drawing set "d".

According to the problem, the pen costs 6 rubles, and the book costs 6 times more than the notebook. Additionally, the drawing set costs 4 times more than the pen, and its cost is equal to the cost of the book.

Based on this information, we can set up the following equations:

p = 6 b = 6n d = 4p = 4 * 6 = 24 b = d

Since the cost of the drawing set is equal to the cost of the book, we can equate b and d:

6n = 24

Solving for n, we get:

n = 24 / 6 = 4

Now, substituting the value of n into the equation for b, we can find the cost of the book:

b = 6n = 6 * 4 = 24

Therefore, the cost of each item is as follows: - Pen: 6 rubles - Book: 24 rubles - Notebook: 4 rubles - Drawing set: 24 rubles

Please let me know if there's anything else I can help you with!