Question

Во дворе кошки и куры. У всех вместе 8 голов и 100 когтей. У кошки на 1 лапе 5 когтей, а у кур 4 когтя. Сколько кошек во дворе? Сколько кур во дворе?

Answer 1

Пусть х кошек, тогда на них приходится х*5когтей*4лап=20х когтей
тогда (8-х) куриц, у них (8-х)*2лапы*4когтя=(8-х)*8=64-8х когтей
20х+64-8х=100 по условию , значит 12х=36 х=3
кошек 3, куриц 5

Answer 2

Problem Analysis

We are given that there are cats and chickens in a courtyard. Together, they have a total of 8 heads and 100 claws. The cat has 5 claws on one paw, while the chicken has 4 claws. We need to determine the number of cats and chickens in the courtyard.

Solution

Let's assume the number of cats in the courtyard is x and the number of chickens is y.

From the given information, we can form two equations:

1. The total number of heads: x + y = 82. The total number of claws: 5x + 4y = 100

To solve this system of equations, we can use substitution or elimination.

Let's solve it using substitution:

From equation 1, we can express x in terms of y: x = 8 - y

Substituting this value of x into equation 2: 5(8 - y) + 4y = 100

Simplifying the equation: 40 - 5y + 4y = 100 40 - y = 100 -y = 100 - 40 -y = 60 y = -60 (multiplying both sides by -1)

Since the number of chickens cannot be negative, this solution is not valid.

Let's try solving it using elimination:

Multiplying equation 1 by 4, we get: 4x + 4y = 32

Subtracting this equation from equation 2: (5x + 4y) - (4x + 4y) = 100 - 32 x = 68

Again, this solution is not valid because the number of cats cannot be 68.

Since neither of the solutions is valid, it seems there is an error in the given information or the problem itself.

Unfortunately, we cannot determine the number of cats and chickens in the courtyard based on the given information.

Please let me know if there is anything else I can help you with.