Question

У Коли и Серёжи было вместе 60 монет.Коля отдал Серёжи 5 монет,и у него стало в 2 раза больше монет,чем у Серёжи.Сколько монет было у Коли и сколько-у Серёжи?

Answer 1

У Коли и Серёжи было вместе 60 монет.Коля отдал Серёжи 5 монет,и у него стало в 2 раза больше монет,чем у Серёжи.Сколько монет было у Коли и сколько-у Серёжи?

Пусть у Коли было х монет, а у Сережи у монет.
Тогда вмесье у них было
                              х+ у =60
После того как Коля отдел Сереже 5 монет у него стало х-5 а у Сережи у+5
Так как у Коли стало в 2 раза больше чем у Сережи то можно записать
      x-5 =2(y+2)
Запишем систему уравнений
{x+y=60
{ x-5 =2(y+5)
Решим систему уравнений методом подстановки
Из первого уравнения найдем х и подставим во второе уравнение
х+у=60 или х =60-у
x-5 =2y+10
60-y-5 = 2y+10 
3y = 55-10
y =45/3
y=15
x=60-15 =45
Проверка
х+у =15+45 =60
 x-5 =2(y+5)
45-5 =2(15+5)
40=40
Поэтому у Коли было 45 монет у Сережи было 15 монет
Ответ:45;15 

Answer 2

Problem Analysis

We are given that Kolya and Sergey had a total of 60 coins. Kolya gave Sergey 5 coins, and as a result, Kolya ended up with twice as many coins as Sergey. We need to determine how many coins Kolya and Sergey had initially.

Solution

Let's assume that Kolya initially had x coins and Sergey initially had y coins.

According to the given information, the following equations can be formed: 1. The sum of their initial coins is 60: x + y = 60. 2. After Kolya gave Sergey 5 coins, Kolya had twice as many coins as Sergey: (x - 5) = 2(y + 5).

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

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From equation 1, we have x = 60 - y.

Substituting this value of x into equation 2, we get: (60 - y - 5) = 2(y + 5).

Simplifying the equation: 55 - y = 2y + 10.

Bringing all the y terms to one side: 3y = 45.

Dividing both sides by 3: y = 15.

Substituting this value of y into equation 1, we get: x + 15 = 60.

Simplifying the equation: x = 45.

Therefore, Kolya initially had 45 coins and Sergey initially had 15 coins.

Answer

Kolya initially had 45 coins and Sergey initially had 15 coins.