Question

6. Якими знаннями і вміннями з математики мають володіти учні, щоб правильно розв’язати таку задачу: «Микола зловив велику щуку. її тулуб важить стільки, скільки голова і хвіст. А дві голови стільки, скільки тулуб і два хвости. Яка маса всієї рибини, якщо хвіст важить 2 кг?»

Answer 1

Mathematics Knowledge and Skills Required to Solve the Problem

To correctly solve the given problem, students need to have a good understanding of basic mathematical concepts such as addition, subtraction, and multiplication. They should also be familiar with the concept of equations and be able to solve simple algebraic equations.

Solution to the Problem

Let's break down the problem and solve it step by step:

1. Let's assume the weight of the fish's body (тулуб) is represented by the variable x. 2. According to the problem, the weight of the head and the weight of the tail together is equal to the weight of the body. So, the weight of the head and the tail combined is also x. 3. The problem also states that the weight of two heads is equal to the weight of the body and two tails combined. So, the weight of two heads is also x. 4. Finally, the problem mentions that the weight of the tail is 2 kg.

Now, we can set up an equation to solve for the weight of the fish's body:

x + x + 2 = x + x + 2x

Simplifying the equation:

2x + 2 = 3x + 2x

2x + 2 = 5x

Subtracting 2x from both sides:

2 = 3x

Dividing both sides by 3:

x = 2/3

Therefore, the weight of the fish's body (тулуб) is 2/3 kg.

To find the total weight of the fish, we need to add the weight of the body, the weight of the head, and the weight of the tail:

Total weight = x + x + 2 + 2 = 2/3 + 2/3 + 2 + 2 = 4/3 + 4 = 16/3 kg

So, the total weight of the fish is 16/3 kg.

Conclusion

To solve the given problem, students need to have a good understanding of basic mathematical concepts such as addition, subtraction, multiplication, and algebraic equations. By breaking down the problem and setting up an equation, we can find the weight of the fish's body and calculate the total weight of the fish. In this case, the weight of the fish's body is 2/3 kg, and the total weight of the fish is 16/3 kg.