Question

Fathers age is three times the sum of the ages of his two children. After 5 years his age will be twice the sum of the ages of two children. Find the fathers age.

Answer 1

father's age is three times the sum of ages of his two children. 
after 5 years his will be twice the sum of the ages of the son.
find the present ages of father and son.
:
Let a = age of the son
Let b = age of the other child
Let f = fathers age
:
"father's age is three times the sum of ages of his two children." 
f = 3(a+b))
f = 3a + 3b
:
"after 5 years his will be twice the sum of ages of the son. "
f + 5 = 2(a + 5)
f + 5 = 2a + 10

f = 2a + 10 - 5
f = 2a + 5
replace f with (3a+3b)
3a + 3b = 2a + 5
3a - 2a = - 3b + 5
a = -3b + 5
Only one positive integer solution; b = 1, (other child's age)
a = -3(1) + 5
a = 2 yrs is the son's present age
then
f = 3(2+1)
f = 9 yrs is father's age, doesn't make sense, but if fits
:
check in the statement
"after 5 year his will be twice the sum of ages of the son."
9 + 5 = 2(2+5)
14 = 2(7)

Answer 2

$\mathfrak{\huge{Answer:}}$

Let age of father = x

Let sum of the ages of the two children be = y

According to the question :-

x = 3y ....(1)

---After 5 years, ages will be----

Father's age = x + 5

Sum of the two children = y + 5 + 5 ( since this "y" comprises ages of two people, the addition needs to be done twice )

According to the question :-

x + 5 = 2 ( y + 10 )

=》 x + 5 = 2y + 20

Due to (1)

=》 3y + 5 = 2y + 20

=》 y = 15

Age of father = 3y = 3 × 15 = 45 years