Question

У двух братьев поровну орехов. Если старший брат отдаст младшему 18 орехов, то орехов у него станет в 5 раз(-а) меньше, чем у младшего. Сколько орехов у каждого брата было первоначально?

Answer 1

Пусть у каждого из братьев изначально было х орехов, тогда:
х + 18 = 5(х -18)
х + 18 = 5х - 90
90 + 18 = 5х - х
108 = 4х
х = 108/4
х = 27
Ответ: первоначально у каждого брата было 27 орехов.

Answer 2

Problem Analysis

We are given that two brothers initially have an equal number of nuts. If the older brother gives 18 nuts to the younger brother, then the number of nuts the older brother has will be 5 times less than the number of nuts the younger brother has. We need to determine the initial number of nuts each brother had.

Solution

Let's assume that the initial number of nuts each brother had is represented by the variables `x` (for the older brother) and `y` (for the younger brother).

According to the problem statement, the older brother gives 18 nuts to the younger brother. After this exchange, the older brother has 5 times fewer nuts than the younger brother. Mathematically, we can represent this as:

x - 18 = (1/5)(y + 18)

Simplifying this equation, we get:

5x - 90 = y + 18

Now, we can solve this equation to find the values of `x` and `y`.

Let's solve the equation:

5x - 90 = y + 18

Rearranging the equation:

5x - y = 108

Now, we have two equations:

x - y = 108/5 -- Equation 1 x - 18 = (1/5)(y + 18) -- Equation 2

We can solve these equations simultaneously to find the values of `x` and `y`.

Solution