Question

В банке сидят жуки и пауки. Их общее число ног – 54, причём у каждого паука по 8 ног, а у каждого жука по 6. Сколько в банках может быть жуков и сколько пауков? Найди все возможные решения.

Answer 1

6х+8у=54
если х=5 то у=3
тогда 5 жуков и 3 пауки
получается 5 жуков 5*6=30 ног
3 пауков 3*8=24
30+24=54 ног вот кароч

Answer 2

Problem Analysis

We are given that there are bugs and spiders in a bank, and the total number of legs is 54. Each spider has 8 legs, and each bug has 6 legs. We need to determine the possible number of bugs and spiders in the bank.

Solution

Let's assume the number of bugs is represented by x and the number of spiders is represented by y.

From the given information, we can form the following equations:

1. The total number of legs is 54: 6x + 8y = 54.

We can solve this system of equations to find the values of x and y.

Solving the Equations

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

Multiplying the first equation by 3 and the second equation by 2, we get:

1. 18x + 24y = 162 2. 12x + 16y = 108

Subtracting equation 2 from equation 1, we get:

6x + 8y = 54 - (12x + 16y = 108) ----------------------- -6x - 8y = -54

Simplifying, we have:

0 = 54 - 108

This equation is not possible to solve because it results in a contradiction. Therefore, there is no solution to the system of equations.

Conclusion

Based on the given information, there is no possible combination of bugs and spiders in the bank that would result in a total of 54 legs.