Question

Найдите НОД(24 ,60,84) распишите пожалуйстаСемья состоит из четырёх человек: матери,отца, сына и дочери.Отец 5 лет старше матери , мать в 4 раза старше сына и в 5 раз старше дочери . Сколько лет каждому, если сумма их возрастов составляет 103? (возраст матери следует принять за 20 частей)

Answer 1

 НОД(24 ,60,84)=12
24=2*2*2*3
60=2*2*3*5
84=2*2*3*7

20х(лет)-мама
20х+5(лет)-папе
20х\4(лет)-сыну
20х\5(лет)-дочери

20х+20х+5+20х\4+20х\5=103
49х+5=103
49х=103-5
49х=98
х=98:49
х=2года-1часть.
20х=20*2=40лет-маме.
20х+5=40+5=45лет-папе.
20х\4=20*2\4=40\4=10лет-сыну.
20х\5=20*2\5=40\5=8лет-дочери.

Answer 2

Calculating the Greatest Common Divisor (GCD)

To find the greatest common divisor (GCD) of 24, 60, and 84, we can use the prime factorization method or the Euclidean algorithm. Let's use the Euclidean algorithm to find the GCD.

The Euclidean algorithm states that the GCD of two numbers a and b is the same as the GCD of b and the remainder when a is divided by b. We can apply this recursively until the remainder is 0.

Let's calculate the GCD of 24, 60, and 84 using the Euclidean algorithm:

24 = 2 * 2 * 2 * 3 60 = 2 * 2 * 3 * 5 84 = 2 * 2 * 3 * 7

Now, we can apply the Euclidean algorithm: ``` GCD(24, 60) = GCD(60, 24) = GCD(24, 12) = GCD(12, 0) = 12 ``` So, the GCD of 24 and 60 is 12.

Next, we find the GCD of 12 and 84: ``` GCD(12, 84) = GCD(84, 12) = GCD(12, 0) = 12 ``` So, the GCD of 12 and 84 is also 12.

Therefore, the GCD of 24, 60, and 84 is 12.

Age Calculation Puzzle

Let's solve the age calculation puzzle for the family consisting of a mother, father, son, and daughter.

Given: - The father is 5 years older than the mother. - The mother is 4 times older than the son. - The mother is 5 times older than the daughter. - The sum of their ages is 103.

Let's denote the age of the mother as 20x (as per the given note), then: - The father's age is 20x + 5. - The son's age is 5x. - The daughter's age is 4x.

Now, we can form the equation: 20x + (20x + 5) + 5x + 4x = 103

Solving for x: 49x + 5 = 103 49x = 98 x = 2

So, the ages are: - Mother: 20x = 20 * 2 = 40 years - Father: 20x + 5 = 40 + 5 = 45 years - Son: 5x = 5 * 2 = 10 years - Daughter: 4x = 4 * 2 = 8 years

Therefore, the ages of the family members are: - Mother: 40 years - Father: 45 years - Son: 10 years - Daughter: 8 years