Question

Брат на 5 лет старше сестры. Найти сумму возрастов брата и сестры, если четыре года назад их возрасты относились как 3: 2

Answer 1

Пусть х лет сейчас сестре
х + 5 лет сейчас брату
х - 4 лет было сестре 4 года назад
х + 5 - 4 = х + 1 лет было брату 4 года назад
Т.к. их возрасты 4 года назад относились как 3:2, получим уравнение
$\frac{x+1}{x-4}= \frac{3}{2}$

Воспользуемся свойством пропорции
2*(х + 1) = 3*(х - 4)
2х + 2 = 3х - 12
2х - 3х = -2 -12
-х = -14
х = -14 : (-1)
х = 14
14 лет сейчас сестре
14 + 5 = 19 лет сейчас брату
14 + 19 = 33 - сумма возрастов брата и снстры

Answer 2

Problem Statement

We are given that a brother is 5 years older than his sister. We need to find the sum of their ages if four years ago their ages were in the ratio of 3:2.

Solution

Let's assume the sister's current age is x years. Since the brother is 5 years older, his current age would be x + 5 years.

Four years ago, the sister's age would have been x - 4 years, and the brother's age would have been (x + 5) - 4 years, which simplifies to x + 1 years.

According to the given information, their ages four years ago were in the ratio of 3:2. Therefore, we can set up the following equation:

(x - 4) / (x + 1) = 3 / 2

To solve this equation, we can cross-multiply:

2(x - 4) = 3(x + 1)

Expanding and simplifying the equation:

2x - 8 = 3x + 3

-x = 11

x = -11

Since age cannot be negative, we can conclude that there is no valid solution for this problem.