Question

Помогите решить только без икса. Три приятеля:Зайцев, Соколов и Ефимов-собрали в коробку жуков и пауков. Всего 10 штук. В коробке оказалось 68 ног. Сколько в коробке жуков и сколько пауков, если известно, что у жука 6 ног , а у паука 8?

Answer 1

Десять жуков и один паук

Answer 2

Problem Analysis

We are given that three friends, Zaytsev, Sokolov, and Efimov, collected a total of 10 insects (beetles and spiders) in a box. The total number of legs in the box is 68, with beetles having 6 legs and spiders having 8 legs. We need to determine the number of beetles and spiders in the box.

Solution

Let's assume the number of beetles in the box is b and the number of spiders is s.

We can set up the following equations based on the given information: 1. The total number of insects in the box is 10: b + s = 10. 2. The total number of legs in the box is 68: 6b + 8s = 68.

We can solve this system of equations to find the values of b and s.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express b in terms of s: b = 10 - s.

Substituting this value of b into equation 2, we get: 6(10 - s) + 8s = 68.

Simplifying the equation: 60 - 6s + 8s = 68, 2s = 8, s = 4.

Now, substituting the value of s back into equation 1, we get: b + 4 = 10, b = 6.

Therefore, there are 6 beetles and 4 spiders in the box.

Answer

There are 6 beetles and 4 spiders in the box.

Verification

Let's verify our answer by checking if the total number of insects and legs in the box match the given information.

The total number of insects is 6 beetles + 4 spiders = 10 insects, which matches the given information.

The total number of legs is (6 legs per beetle * 6 beetles) + (8 legs per spider * 4 spiders) = 36 + 32 = 68 legs, which also matches the given information.

Therefore, our answer is verified.