# 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 result:

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

#### Solution:

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 would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

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?

## Next similar math problems:

• Father and sons
Father is 27 and his sons 2 and one year. In how many years will his sons sum up to half his age?
• Father 7
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 sons
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
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
Father is 36 years old, 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?
• Family and age ratios
Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother?
• The 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
• Age problems
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
• Population 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?
• The sum
The sum of the first 10 members of the arithmetic sequence is 120. What will be the sum if the difference is reduced by 2?
• Father and son
When I was 11, my father was 35 years old. Today, my father has three times more years than me. How old is she?
• Three siblings
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?