Question

Сестра 4 года назад была старше брата в 1,5 раза,а через 6 лет она будет старше брата на 25%. сколько лет сестре и брату

Answer 1

Возьмем за х возраст сестры, а за у - брата, тогда получим систему уравнений:
х-4=(у-4)*1,5 и х+6=(у+6)/0,75
х-4=1,5у-6 и 0,75х+4,5=у+6
х-1,5у=-2 и 0,75х-у=1,5
Из первого уравнения х=-2+1,5у
Домножим второе уравнение на 100, то есть 75х-100у=150 и подставим х
75(-2+1,5у)-100у=150
-150+112,5у-100у=150
12,5у=300
у=24
х=34

Answer 2

Problem Analysis

We are given that 4 years ago, the sister was 1.5 times older than the brother, and in 6 years, she will be 25% older than the brother. We need to determine the ages of the sister and the brother.

Solution

Let's assume the current age of the brother is B and the current age of the sister is S.

From the given information, we can form two equations:

Equation 1: 4 years ago, the sister was 1.5 times older than the brother. Equation 2: In 6 years, the sister will be 25% older than the brother.

Equation 1: 4 years ago, the sister was 1.5 times older than the brother.

If we subtract 4 from the current ages of the sister and the brother, we can write the equation as:

(S - 4) = 1.5 * (B - 4)

Equation 2: In 6 years, the sister will be 25% older than the brother.

If we add 6 to the current ages of the sister and the brother, we can write the equation as:

(S + 6) = 1.25 * (B + 6)

Now, we have a system of two equations with two variables. We can solve this system to find the ages of the sister and the brother.

Let's solve the system of equations:

(S - 4) = 1.5 * (B - 4) (Equation 1)

(S + 6) = 1.25 * (B + 6) (Equation 2)

Expanding Equation 1:

S - 4 = 1.5B - 6

S = 1.5B - 6 + 4

S = 1.5B - 2 (Equation 3)

Substituting Equation 3 into Equation 2:

(1.5B - 2 + 6) = 1.25 * (B + 6)

1.5B + 4 = 1.25B + 7.5

1.5B - 1.25B = 7.5 - 4

0.25B = 3.5

B = 3.5 / 0.25

B = 14

Substituting the value of B into Equation 3:

S = 1.5 * 14 - 2

S = 21 - 2

S = 19

Therefore, the current age of the sister is 19 years and the current age of the brother is 14 years.

Answer

The sister is currently 19 years old and the brother is currently 14 years old.