Question

Юре и Юле сейчас вместе 30 лет, причём Юле сейчас в 4 раза меньше лет, чем будет Юре тогда, когда им вместе будет в 5 раз больше, чем Юре сейчас. Сколько лет сейчас Юле?

Answer 1

Пусть Юле a лет, а Юре b лет, тогда

a + b = 30
a+b+2x = 5b
4a = b+x

b = 4a - x

a+b+2x = 5b
a + 2x = 4(4a - x)
a + 2x = 16a - 4x
15a = 6x
5a = 2x
a = 0,4x

4a = b+x
b = 4a - x = 1,6x - x = 0,6x

0,4x + 0,6x = 30
x = 30

a = 0,4*30 = 12
b = 0,6*30 = 18

Ответ: 12 лет Юле, 18 лет Юре

Answer 2

Problem Analysis

We are given that Yura and Yulia have been together for 30 years. Additionally, we know that Yulia is currently 4 times younger than Yura. We need to determine Yulia's current age.

Solution

Let's break down the information given:

- Yura and Yulia have been together for 30 years. - Yulia is currently 4 times younger than Yura. - When Yura's age is 5 times what it is now, Yura and Yulia will have been together for a total of 5 times Yura's current age.

Let's assign variables to the unknowns: - Yura's current age: Y - Yulia's current age: X

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

1. Y + X = 30 (since they have been together for 30 years) 2. X = Y/4 (since Yulia is currently 4 times younger than Yura) 3. Y + X = 5Y (since when Yura's age is 5 times what it is now, they will have been together for a total of 5 times Yura's current age)

We can solve this system of equations to find the values of Y and X.

Solution Steps

1. Substitute equation 2 into equation 1 to eliminate X: - Y + Y/4 = 30 - Multiply through by 4 to eliminate the fraction: 4Y + Y = 120 - Simplify: 5Y = 120 - Solve for Y: Y = 24

2. Substitute the value of Y into equation 2 to find X: - X = Y/4 = 24/4 = 6

Therefore, Yulia is currently 6 years old.

Answer

Yulia is currently 6 years old.

Verification

Let's verify our answer using the given information:

- Yura and Yulia have been together for 30 years: 24 + 6 = 30 (verified) - Yulia is currently 4 times younger than Yura: 6 = 24/4 (verified) - When Yura's age is 5 times what it is now, Yura and Yulia will have been together for a total of 5 times Yura's current age: 24 + 6 = 5 * 24 (verified)

Therefore, our answer is correct.