Question

Брат и сестра имеют по некоторой сумме денег . Если брат отдаст сестре 24р то у них станет денег поровну. Если же сестра отдаст брату 27р то у брата окажется в 2 раза больше денег чем у сесты. Сколько денег у каждого

Answer 1

Пусть Х рублей - количество денег у сестры тогда У рублей - количество денег у брата У - 24 = Х + 24 - брат отдал сестре 24 рубля. 2 * (Х - 27) = У + 27 - сестра отдала брату 24 рубля, денег у брата стало в 2 раза больше У - Х = 48. 2Х - 54 = У + 27. 2Х - У = 81 Получается система уравнений: У - Х = 48 2Х - У = 81 У = 48 + Х (подставляем во второе уравнение вместо У) 2Х - (48 + Х) = 81 2Х - 48 - Х = 81 Х = 129 рублей - денег у сестры У = 48 + 129 = 177 рубля - денег у брата

Answer 2

Problem Analysis

We are given that a brother and sister have a certain amount of money. If the brother gives the sister 24 rubles, they will have an equal amount of money. However, if the sister gives the brother 27 rubles, the brother will have twice as much money as the sister. We need to determine how much money each of them has.

Solution

Let's assume the brother has B rubles and the sister has S rubles.

According to the given information: 1. If the brother gives the sister 24 rubles, they will have an equal amount of money. This can be expressed as: B - 24 = S + 24. 2. If the sister gives the brother 27 rubles, the brother will have twice as much money as the sister. This can be expressed as: B + 27 = 2(S - 27).

We can solve these two equations to find the values of B and S.

Solving the Equations

Let's solve the equations step by step:

1. From equation 1, we have: B - 24 = S + 24. - Rearranging the equation, we get: B - S = 48. (Equation 3)

2. From equation 2, we have: B + 27 = 2(S - 27). - Expanding the equation, we get: B + 27 = 2S - 54. - Rearranging the equation, we get: B - 2S = -81. (Equation 4)

Now, we have a system of equations with two variables (B and S). We can solve this system to find the values of B and S.

To solve the system, we can use the method of substitution or elimination. Let's use the method of elimination:

3. Subtracting equation 4 from equation 3, we get: (B - S) - (B - 2S) = 48 - (-81). - Simplifying the equation, we get: -S + 2S = 48 + 81. - Combining like terms, we get: S = 129.

Now that we have the value of S, we can substitute it back into one of the original equations to find the value of B.

4. Substituting S = 129 into equation 3, we get: B - 129 = 48. - Solving for B, we get: B = 177.

Therefore, the brother has 177 rubles and the sister has 129 rubles.

Answer

The brother has 177 rubles and the sister has 129 rubles.

Please note that the solution provided is based on the given information and the assumption that the initial amounts of money possessed by the brother and sister are positive integers.