Question

A man has two children.The man's age is 3 times the sum of the children age

Answer 1

Answer:

x = man's age

y = sum of son's ages

 

man is 3 times as old as sum of sons ages

x = 3y   {equation 1}

 

5 years hence (from now) he will be double

the sum of sons ages.  Since y represents the 

sum of 2 ages, in 5 years y will increase by 10.

 

x + 5 = 2(y + 10)

x + 5 = 2y + 20

x = 2y + 15   {equation 2}

 

since x also equals 3y then

 

3y = 2y+15

y = 15

 

x = 3y = 45

 

The man is 45 years old.

 

check:

x+5 = 2(y+10)

50 = 2(25)

50 = 50

Answer 2

Let the age of father be x years and sum of the ages of his children by y years.

After 5 years,

Father's age = (x + 5) years

Sum of ages of his children = (y + 10) years

From the given information, we have:

x = 3y ...(1)

and x + 5 = 2(y + 10)

x - 2y = 15 ...(2)

From (1) and (2), we have,

3y - 2y = 15 y = 15

x = 3y = 45

Father's age = 45 years

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