Question

Троє чоловіків на питання скільки кожному років,відповіли по-різному. Короленко: - Нам разом - 135 років; Гуревич: - Я молодший за Короленка на 10 років; Данилюк: - Мені разом з Короленком 85 років. Скільки років кожному?

Answer 1

Пусть Короленко - х лет, тогда Гуревичу - (х-10), а Данилюку - (85-х)

х+ (х-10) +(85-х) = 135
х+х-10+85-х=135
х+75 = 135
х = 135-75 = 60 лет Короленко
60-10 = 50 лет Гуревичу
85-60 =25 лет Данилюку

Answer 2

Problem Analysis

We are given the ages of three individuals: Korolenko, Gurevich, and Danyliuk. We need to determine the age of each person based on the given information.

Solution

Let's break down the given information and solve the problem step by step.

1. Korolenko says, "Together we are 135 years old." 2. Gurevich says, "I am 10 years younger than Korolenko." 3. Danyliuk says, "Together with Korolenko, I am 85 years old."

Let's assign variables to the ages of each person: - Korolenko's age: K - Gurevich's age: G - Danyliuk's age: D

Based on the given information, we can form the following equations:

1. Equation 1: K + G + D = 135 (Korolenko's statement) 2. Equation 2: G = K - 10 (Gurevich's statement) 3. Equation 3: K + D = 85 (Danyliuk's statement)

To solve these equations, we can use a system of linear equations.

Substituting Equation 2 into Equation 1, we get: (K - 10) + K + D = 135 2K + D = 145 (Equation 4)

Substituting Equation 2 into Equation 3, we get: (K - 10) + D = 85 K + D = 95 (Equation 5)

Now we have a system of two equations with two variables (Equations 4 and 5). We can solve this system to find the values of K and D.

Subtracting Equation 5 from Equation 4, we get: (2K + D) - (K + D) = 145 - 95 K = 50

Substituting the value of K into Equation 5, we get: 50 + D = 95 D = 45

Now that we have the values of K and D, we can substitute them into Equation 2 to find the value of G: G = K - 10 G = 50 - 10 G = 40

Therefore, the ages of the three individuals are: - Korolenko: 50 years old - Gurevich: 40 years old - Danyliuk: 45 years old

Answer

Based on the given information, Korolenko is 50 years old, Gurevich is 40 years old, and Danyliuk is 45 years old.