Question

В клетке сидят фазаны и кролики. Известно, что у них 35 голов и 94 ноги. Определить количество фазанов и кроликов.

Answer 1

Пусть будет х - фазанов и у - кроликов, тогда 2х - ног у фазанов и 4у - ног у кроликов. Так как у всех по одной голове, можем составить систему уравнений: система: х+у=35 и 2х+4у=94; пешим систему подстановкой: х=35-у; 2*(35-у)+4у=94; 70-2у+4у=94; 2у=24; у=12; х=35-12=23. Ответ: 23 фазана и 12 кроликов.

Answer 2

Problem Analysis

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

Solution

Let's assume that the number of pheasants is represented by 'p' and the number of rabbits is represented by 'r'. We can set up a system of equations based on the given information:

Equation 1: p + r = 35 (since the total number of heads is 35) Equation 2: 2p + 4r = 94 (since each pheasant has 2 legs and each rabbit has 4 legs)

We can solve this system of equations to find the values of 'p' and 'r'.

Solution Steps

1. Solve Equation 1 for 'p': p = 35 - r 2. Substitute the value of 'p' in Equation 2: 2(35 - r) + 4r = 94 3. Simplify the equation: 70 - 2r + 4r = 94 4. Combine like terms: 2r = 24 5. Solve for 'r': r = 12 6. Substitute the value of 'r' in Equation 1 to find 'p': p + 12 = 35 7. Solve for 'p': p = 23

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

Answer: There are 23 pheasants and 12 rabbits in the cage.

Explanation

By solving the system of equations, we found that there are 23 pheasants and 12 rabbits in the cage. This solution satisfies the given conditions of 35 heads and 94 legs.