Question

Катя посчитала, что сейчас суммарный возраст её, её папы, мамы и младшего брата равен 76 годам (других детей в семье нет). Мама сказала, что пять лет назад суммарный возраст членов семьи был равен 58 годам. А папа добавил, что десять лет назад он был равен 45 годам. Определите, сколько лет сейчас Кате.

Answer 1

76-5=71
71-58=13
13 лет Кате

Answer 2

Problem Analysis

We are given the information that the current combined age of Katya, her father, her mother, and her younger brother is 76 years. Five years ago, the combined age of the family members was 58 years, and ten years ago, the combined age was 45 years. We need to determine Katya's current age.

Solution

Let's assume Katya's current age is x years.

According to the given information, the combined age of the family members five years ago was 58 years. This means that the sum of their ages five years ago was 58. We can express this as an equation:

(x - 5) + (father's age - 5) + (mother's age - 5) + (brother's age - 5) = 58

Similarly, the combined age of the family members ten years ago was 45 years. We can express this as another equation:

(x - 10) + (father's age - 10) + (mother's age - 10) + (brother's age - 10) = 45

Finally, the current combined age of the family members is 76 years. We can express this as a third equation:

x + father's age + mother's age + brother's age = 76

We now have a system of three equations with three unknowns (x, father's age, mother's age, and brother's age). We can solve this system of equations to find the values of the unknowns.

Let's solve the system of equations step by step:

1. Simplify the equations by removing the parentheses:

x - 5 + father's age - 5 + mother's age - 5 + brother's age - 5 = 58 x - 10 + father's age - 10 + mother's age - 10 + brother's age - 10 = 45 x + father's age + mother's age + brother's age = 76

2. Combine like terms:

x + father's age + mother's age + brother's age - 20 = 58 x + father's age + mother's age + brother's age - 30 = 45 x + father's age + mother's age + brother's age = 76

3. Rearrange the equations to isolate x:

x = 58 + 20 - father's age - mother's age - brother's age x = 45 + 30 - father's age - mother's age - brother's age x = 76 - father's age - mother's age - brother's age

4. Substitute the expressions for x in the second and third equations:

58 + 20 - father's age - mother's age - brother's age = 45 + 30 - father's age - mother's age - brother's age 76 - father's age - mother's age - brother's age = 76 - father's age - mother's age - brother's age

5. Simplify the equations:

78 - father's age - mother's age - brother's age = 75 - father's age - mother's age - brother's age 0 = 0

The last equation is always true, which means that the system of equations is dependent. This means that there are infinitely many solutions, and we cannot determine the exact values of the unknowns.

Therefore, we cannot determine Katya's current age based on the given information.

Please let me know if I can help you with anything else.