Question

Сёстрам Саше, Даше и Наташе столько лет, что, если половину возраста Саши сложить счетвертью возраста Даши и восьмой частью возраста Наташи, получится столько лет, сколько исполнится Саше через год; а если бы Саша была в пять раз старше, то ей было бы на 44 года больше, чем Даше. Сколько лет Саше, Даше и Наташе вместе?​

Answer 1

Ответ:

Даше 42 Наташи 44 а Саше 43

Answer 2

Problem Analysis

We are given information about the ages of three sisters, Sasha, Dasha, and Natasha. We need to determine their combined ages. The problem provides two conditions: 1. If we add half of Sasha's age to a quarter of Dasha's age and an eighth of Natasha's age, the result will be the same as Sasha's age in one year. 2. If Sasha were five times older, she would be 44 years older than Dasha.

Solution

Let's assume the current ages of Sasha, Dasha, and Natasha are S, D, and N, respectively.

Condition 1 states that if we add half of Sasha's age to a quarter of Dasha's age and an eighth of Natasha's age, the result will be the same as Sasha's age in one year. Mathematically, this can be represented as:

S + (S/2) + (D/4) + (N/8) = S + 1

Simplifying the equation, we get:

(S/2) + (D/4) + (N/8) = 1

Condition 2 states that if Sasha were five times older, she would be 44 years older than Dasha. Mathematically, this can be represented as:

S + 44 = 5D

Now we have two equations with two unknowns (S and D). We can solve these equations to find the values of S and D.

Solving the Equations

Let's solve the equations using substitution or elimination method.

From equation 2, we can express S in terms of D:

S = 5D - 44

Substituting this value of S in equation 1, we get:

((5D - 44)/2) + (D/4) + (N/8) = 1

Multiplying the equation by 8 to eliminate the fractions, we get:

4(5D - 44) + 2D + N = 8

Simplifying the equation, we get:

20D - 176 + 2D + N = 8

Combining like terms, we get:

22D + N = 184

Now we have a new equation relating D and N.

Conclusion

We have two equations: 1. S = 5D - 44 2. 22D + N = 184

We need to find the values of S, D, and N that satisfy both equations. Unfortunately, the problem does not provide enough information to determine the exact ages of Sasha, Dasha, and Natasha.