Question

Вася сказал Диме: "Отдай мне 8 рублей и у меня денег станет больше, чем у тебя в 2 раза". А Дима возразил: "Дай лучше ты мне 8 руб., тогда у нас денег будет одинаковое количество". Сколько денег у каждого мальчика?

Answer 1

Получается система уравнений (пусть х - деньги васи, у - деньги димы)
x + 8 = 2*(y - 8)
x - 8 = y + 8
Решаем методом подстановки
x = y - 16
y + 16 + 8 = 2*(y - 8)
y + 24 = 2y - 16
y = 40
x - 8 = 40 + 8
x = 56
Ответ: у Васи было 56 руб., у Димы - 40.

Answer 2

Problem Analysis

Vasya claims that if Dima gives him 8 rubles, then Vasya will have more money than Dima by a factor of 2. However, Dima disagrees and suggests that if Vasya gives him 8 rubles instead, then they will have an equal amount of money. We need to determine how much money each boy currently has.

Solution

Let's assume that Vasya currently has x rubles and Dima has y rubles.

According to Vasya's claim, if Dima gives him 8 rubles, then Vasya will have more money than Dima by a factor of 2. This can be expressed as the equation:

x + 8 = 2(y - 8)

According to Dima's suggestion, if Vasya gives him 8 rubles, then they will have an equal amount of money. This can be expressed as the equation:

x - 8 = y + 8

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 substitution:

From the second equation, we can express x in terms of y:

x = y + 16

Substituting this value of x into the first equation:

(y + 16) + 8 = 2(y - 8)

Simplifying the equation:

y + 24 = 2y - 16

Bringing all the terms to one side:

2y - y = 24 + 16

Simplifying further:

y = 40

Substituting this value of y back into the equation x = y + 16:

x = 40 + 16

Simplifying:

x = 56

Therefore, Vasya has 56 rubles and Dima has 40 rubles.

Answer

Vasya has 56 rubles and Dima has 40 rubles.