Question

Five years ago, a father was six times as old as his son. Two years hence, the age of the father will be 1 year more the three times then age of his son. Find their present ages.​

Answer 1

The dad is 35 and the son is 10

Explanation:

Let f = the father's age

let s - the son's age

In the equations f-5 and s-5 represents the father and son's ages 5 years ago. f + 2 and s +2 represent the father and son's ages two years in the future.

Answer 2

84

Explanation:

Let's call the father's present age "F" and the son's present age "S".

Five years ago, the father's age was F - 5 and the son's age was S - 5.

According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.

Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.

According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.

We can now substitute the first equation into the second:

3S + 7 = 6S - 28,

3S - 6S = -35 - 7 = -42,

-3S = -42,

S = 14.

Finally, the father's present age is F = 6S - 35 = 84.