Question

У семейной пары дни рождения в один и тот же день. При очередном праздновании их общего дня рождения муж заметил, что сейчас ему вдвое больше лет, чем было его жене тогда, когда ему было столько лет, сколько жене сейчас. А когда ей будет столько лет, сколько ему теперь, им обоим вместе будет 81 год. Сколько лет мужу сейчас?

Answer 1

X возраст мужа
y возраст жены
2(y(x-y)=x
x+(x+(x-y))=81-система
4y-2x=x
3x-y=81
4(3x-81)-3x=0
9x=324
x=36
36 лет мужу

Answer 2

Problem Analysis

We have a couple who share the same birthday. During their joint birthday celebration, the husband realizes that he is now twice as old as his wife was when he was the same age as she is now. Additionally, when his wife reaches his current age, their combined age will be 81 years. We need to determine the current age of the husband.

Solution

Let's assume the current age of the husband is H and the current age of the wife is W.

From the given information, we can derive the following equations:

1. The husband is now twice as old as his wife was when he was the same age as she is now: - H = 2(W - (H - W)) 2. When the wife reaches the husband's current age, their combined age will be 81 years: - W + (H - W) + H = 81

We can solve these equations to find the current age of the husband.

Solving the Equations

Let's substitute equation 1 into equation 2 and solve for W:

W + (H - W) + H = 81

2W + H = 81

W = 81 - H (equation 3)

Substituting equation 3 into equation 1, we can solve for H:

H = 2((81 - H) - (H - (81 - H)))

H = 2(81 - H - H + 81 - H)

H = 2(162 - 3H)

H = 324 - 6H

7H = 324

H = 324 / 7

H ≈ 46.29

Therefore, the current age of the husband is approximately 46.29 years.

Answer

The current age of the husband is approximately 46.29 years.