Max is 24 years older than his son, Liam. In two years Liam will be half as old as Max. How old is Liam now?

Question

Max is 24 years older than his son, Liam. In two years Liam will be half as old as Max.  How old is Liam now?

Answer 1

Let M be Max's age now and L be Liam's age now.

Currently, Max is 24 years older than Liam, or in equation form:

 

(Eq 1)  M = 24 + L

 

In 2 years, Liam will be half as old as Max. Both Liam and Max will be 2 years older than they are currently, or in equation form:

 

(Eq 2)  (L + 2) = (M + 2)/2

 

We can substitute M=24+L  from (Eq 1) into (Eq 2) to have:

 

(Eq 3)  (L + 2) = ({24 + L} + 2)/2

 

Solving for L by multiplying both sides by '2' we have

 

2*(L+2) = (24+L+2)

 

or:

 

2*L + 4 = 26 + L

 

rearranging constants and L terms we find that

 

L = 22

or that Liam is currently 22 years old (and Max is currently 46) and in 2 years they will be 24 and 48 years of age.

Answer 2

Lets say that Liam is L years old now, and Max is M years old now...

 

Then M=L+24, today.

 

In two years, Liam will be L+2 years old and Max will be M+2 years old...since Liam will be half as old as Max in 2 years, 

 

L+2 = (M+2)/2 (or 2L+4=M+2 or M=2L+2)

 

If M=L+24 and M=2L+2, then L+24=2L+2, or in other words L=22

 

So Liam is 22 years old right now!

 

We can check that this all works by finding M, M=L+24=22+24=46...Thus Max is 24 years older than Liam today, and in two years, when Liam is 24 and Max is 48, Liam will be half as old as his father!