Question

У брата и сестры было вместе 75 марок. Сестра отдала брату 10 марок,и у нее стало в 2 раза меньше, чем у брата. Сколько марок было у брата и сколько- у сестры?

Answer 1

у сестры - х марок

у брата - (75-х) марок

составим уравнение

2(х-10)=75-х+10

2х-20=85-х

2х+х=85+20

3х=105

х=105/3

х=35 было у сестры

75-35=40 было у брата

Answer 2

Problem Analysis

We are given that the brother and sister had a total of 75 marks. The sister gave 10 marks to the brother, and after that, the sister had half as many marks as the brother. We need to determine how many marks the brother and sister had initially.

Solution

Let's assume that the brother initially had x marks and the sister initially had y marks.

According to the given information, we have two equations:

1. The total marks they had together: x + y = 75. 2. After the sister gave 10 marks to the brother, the sister had half as many marks as the brother: y - 10 = (x - 10) / 2.

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

Solving the Equations

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

From equation 1, we have x = 75 - y.

Substituting this value of x into equation 2, we get:

(75 - y) - 10 = ((75 - y) - 10) / 2.

Simplifying this equation, we have:

65 - y = (65 - y) / 2.

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:

130 - 2y = 65 - y.

Simplifying further, we have:

y = 65.

Substituting this value of y into equation 1, we get:

x + 65 = 75.

Simplifying, we have:

x = 10.

Answer

Therefore, the brother initially had 10 marks and the sister initially had 65 marks.

Verification

Let's verify our answer using the given information.

According to the given information, the sister gave 10 marks to the brother. After this transaction, the sister had half as many marks as the brother.

Initially, the brother had 10 marks and the sister had 65 marks.

After the sister gave 10 marks to the brother, the brother had 20 marks and the sister had 55 marks.

The sister indeed had half as many marks as the brother.

Therefore, our answer is verified.

Conclusion

The brother initially had 10 marks and the sister initially had 65 marks.