Question

Антон старше своего брата на 4 года,и младше своей матери в 5 раз.А его брат младше отца в 4 раза.Сколько лет каждому из братьев ,если всем четверым 86 лет?

Answer 1

Пусть Антону х лет. тогда его брату х+4 года, а его матери 5х лет, а отцу (х+4)·4 года.Вместе им 86 лет составляем уравнение х+х+4+5х+4(х+4)=86   х+х+4+5х+4х+16=86    11х=86-4-16      11х=66   х=6 Антону 6 лет    его брату 6+4=10 лет    5·6=30 лет маме    10·4=40 лет отцу 

Answer 2

Calculation of Ages

To solve this problem, let's assign variables to the ages of the individuals involved. Let's call Anton's age A, his brother's age B, his mother's age M, and his father's age F.

We are given the following information:

1. Anton is 4 years older than his brother: A = B + 4. 2. Anton is 5 times younger than his mother: A = M / 5. 3. Anton's brother is 4 times younger than his father: B = F / 4. 4. The sum of the ages of all four individuals is 86: A + B + M + F = 86.

Now, let's solve these equations to find the ages of each individual.

Substituting equation 1 into equation 2, we get:

B + 4 = M / 5.

Substituting equation 3 into equation 4, we get:

A + F / 4 + M + F = 86.

Let's solve these equations step by step:

1. From equation 1, we have A = B + 4. 2. Substituting this into equation 2, we get B + 4 = M / 5. 3. Rearranging equation 3, we have B = F / 4. 4. Substituting equations 1 and 3 into equation 4, we get (B + 4) + F / 4 + M + F = 86. 5. Simplifying equation 4, we have B + F / 4 + M + F = 82. 6. Rearranging equation 5, we get B + M + (5/4)F = 82. 7. Substituting equation 3 into equation 6, we get (F / 4) + M + (5/4)F = 82. 8. Simplifying equation 7, we have (9/4)F + M = 82. 9. Rearranging equation 8, we get M = 82 - (9/4)F. 10. Substituting equation 9 into equation 2, we get B + 4 = (82 - (9/4)F) / 5. 11. Simplifying equation 10, we have B = (82 - (9/4)F) / 5 - 4. 12. Substituting equation 11 into equation 1, we get A = ((82 - (9/4)F) / 5 - 4) + 4.

Now, we can solve for the ages of Anton (A) and his brother (B) by substituting the values of F, M, and B into equation 12.

Let's calculate the ages of Anton and his brother using the given information.

Calculation Steps:

1. Let's assume Anton's father's age (F) to be a multiple of 4, such as 40. 2. Substituting F = 40 into equation 11, we get B = ((82 - (9/4) * 40) / 5 - 4). 3. Calculating B, we have B = 6. 4. Substituting B = 6 into equation 1, we get A = 6 + 4. 5. Calculating A, we have A = 10.

Therefore, Anton is 10 years old, and his brother is 6 years old.

Please note that these calculations are based on the given information and assumptions made. The actual ages may vary depending on the specific values of F, M, and B.