Question

solve the following problems using two variables: A father is three times as old as his son. 5 years ago father's age was four times his son's age then . Find their present age.​

Answer 1

Answer:

Step-by-step explanation:

Let the son's age be x.

Father's age =3x

∴3x−5=4(x−5)

or 3x−5=4x−20

or 20−5=4x−3x or x=15

After 5 years, son's age is x+5=15+5=20.

Father's age is 3x+5=45+5=50 which is 30 years more than son's age.

Answer 2

Solution :

Let the present age of son's be r years.

Let the present age of Father's be 3r years.

A/q

$\underbrace{\bf{5\:years\:ago\::}}}$

The age of Son's was (r - 5) years.

The age of father's was (3r - 5) years.

$\longrightarrow\tt{(3r-5) = 4(r-5)}\\\\\longrightarrow\tt{3r-5=4r-20}\\\\\longrightarrow\tt{3r-4r=-20+5}\\\\\longrightarrow\tt{\cancel{-}r=\cancel{-}15}\\\\\longrightarrow\bf{r=15\:years}$

Thus;

$\boxed{\sf{The\:present\:age\:of\:son's\: be \:=r = \boxed{\bf{15\:years.}}}}}\\\boxed{\sf{The\:present\:age\:of\:Father's\: be \:=3r = 3\times 15=\boxed{\bf{45\:years.}}}}}$