Question

У трьох кошиках лежать горіхи. У першому на 6 горіхів менше, ніж у двох інших разом. У другому на 10 менше , ніж у першому і третьому разом. Скільки горіхів у третьму кошику?

Answer 1

У трьох кошиках лежать горіхи. У першому на 6 горіхів менше, ніж у двох інших разом. У другому на 10 менше , ніж у першому і третьому разом. Скільки горіхів у третьму кошику?

Answer 2

Problem Analysis

We are given three baskets of nuts. The first basket has 6 fewer nuts than the sum of the nuts in the other two baskets. The second basket has 10 fewer nuts than the sum of the nuts in the first and third baskets. We need to determine the number of nuts in the third basket.

Solution

Let's assume the number of nuts in the first, second, and third baskets are represented by variables x, y, and z, respectively.

According to the given information: 1. The first basket has 6 fewer nuts than the sum of the nuts in the other two baskets. This can be represented as: x = (y + z) - 6. 2. The second basket has 10 fewer nuts than the sum of the nuts in the first and third baskets. This can be represented as: y = (x + z) - 10.

We can solve these two equations simultaneously to find the values of x, y, and z.

Let's substitute the value of x from the first equation into the second equation: ((y + z) - 6) + z - 10 = y

Simplifying the equation: y + z - 6 + z - 10 = y 2z - 16 = 0 2z = 16 z = 8

Therefore, there are 8 nuts in the third basket.

Answer

There are 8 nuts in the third basket.