The ages

The ages of the four sons make an arithmetic sequence, the sum of which is the age of the father today. In three years, the father's age will be the sum of the ages of the three eldest sons, and in the next two years and three months, the father's age will be the sum of the ages of the three youngest sons. What are the ages of all five people today?

Correct answer:

a =  6
b =  8
c =  10
d =  12
f =  36
x =  2

Step-by-step explanation:


b=a+x
c = b+x
d = c+x
f = a+b+c+d
f+3 = (b+3)+(c+3)+(d+3)
f+5 = 2+(a+5)+(b+5)+(c+5)

a-b+x = 0
b-c+x = 0
c-d+x = 0
a+b+c+d-f = 0
b+c+d-f = -6
a+b+c-f = -12

a = 6
b = 8
c = 10
d = 12
f = 36
x = 2

Our linear equations calculator calculates it.



We will be pleased if You send us any improvements to this math problem. Thank you!



avatar




Tips to related online calculators
Do you have a system of equations and looking for calculator system of linear equations?
Do you want to convert time units like minutes to seconds?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • Father and sons
    family Father is 27 and his sons 2 and one year. In how many years will his sons sum up to half his age?
  • Father and sons
    family_7 After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now?
  • Ages 2
    time_13 A man's age is 4 times his son's age. After 5 years he will be just twice his son's age, find their ages.
  • Ages
    calendar Father is 36 years old, and his daughter is 4 years old. Write down the ratio of the age of father and daughter. In what ratio will the ages of father and daughter after 4 years?
  • The family
    family How old is a mother if she is four times older than her daughter and 5 years ago she was even seven times older than her daughter? Today, a son is 30 years younger than a father. 7 years ago, a father was seven times older than a son. How old is a son tod
  • Father and son
    Rodina-01_1 When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?
  • Father 7
    family_8 Father is six times older than his son. After four years, the father will only be four times older. What are their present ages?
  • Father and son
    age When I was eight years old, my father was 30 years old. Today, my father is 3 times more than me. How old am I?
  • Digits of age
    babka The product of the digits of Andrew age as 6 years ago and not equal to 0. Andrew's age is also the youngest possible age with these two conditions. After how many years will the product of the digits of Andrew age again the same as today?
  • Age problems
    time_1 A) Alex is 3 times as old as he was 2 years ago. How old is he now? b) Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey? c) Jessica is 4 years younger than Jennifer now. In 10 years, Jessica will
  • Family and age ratios
    family_1 The age of father and son are in the ratio 10:3; the age of father and daughter are in the ratio 5:2. How old are father and son if the daughter is 20 years old? In what ratio is age sister and brother?
  • Three siblings
    brothers Three siblings have birthday in one day-today. Together they have 35 years today. The youngest is three years younger than middle and the oldest is 5 years older than middle. How old is each?
  • Carla
    family Carla is 5 years old, and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's and Jim's age. Find the present age of each one of them.
  • Two ages
    twodigits_1 Gabrielle is 9 years younger than Mikhail. The sum of their ages is 87. What is Mikhail's age?
  • Population growth
    exp_growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
  • Sequences AP + GP
    seq_sum The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
  • When I
    age When I am as old as my older brother is today, my brother will be twice as old as I am today. a) How old is my brother if I am 8 years old today? b) How old am I if my brother is 21 today?