Question

В клетке находятся фазаны и кролики. Известно, что у них всего 35 голов и 94 ноги. Узнайте число фазанов и кроликов. Действия напишите с пояснениями.

Answer 1

У фазана 2 ноги и 1 голова
У кролика 4 ноги и 1 голова
Т.к. голов всего 35, то и животных всего 35
Пусть фазанов Х, тогда кроликов - У
Имеем:
1) Х+У = 35
2Х + 4У = 94
2) У = 35 - Х
2х + 4*(35-Х) = 94
2х + 140 - 4х = 94
-2х = -46
х = 23, тогла у = 35 - х = 35 - 23 = 12
ОТВЕТ: 23 фазана и 12 кроликов

Answer 2

Problem Analysis

We are given that there are pheasants and rabbits in a cage, and the total number of heads is 35 and the total number of legs is 94. We need to find the number of pheasants and rabbits in the cage.

Solution

Let's assume the number of pheasants is x and the number of rabbits is y. We can set up the following equations based on the given information:

1. The total number of heads: x + y = 35. 2. The total number of legs: 2x + 4y = 94.

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

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 have x = 35 - y.

Substituting this value of x into equation 2, we get:

2(35 - y) + 4y = 94.

Simplifying the equation:

70 - 2y + 4y = 94.

Combining like terms:

2y = 24.

Dividing both sides by 2:

y = 12.

Substituting this value of y back into equation 1, we get:

x + 12 = 35.

Simplifying the equation:

x = 35 - 12.

Calculating:

x = 23.

Answer

Therefore, there are 23 pheasants and 12 rabbits in the cage.

Explanation

The number of pheasants is 23 because we found that x = 23. The number of rabbits is 12 because we found that y = 12.

Verification

Let's verify our solution by checking if the total number of heads and legs match the given information.

The total number of heads is 23 + 12 = 35. The total number of legs is 2(23) + 4(12) = 46 + 48 = 94.

The total number of heads and legs match the given information, so our solution is correct.