How old is each of them now?

Question

Mr. Nelson is 9 times as old as his son, John. In 9 years' time, Mr.NeLeon will be 3 times as old as his son. How old is each of them now?

Answer 1

Let Mr. Nelson's age be m, and his son John be j:

 

Then, the first equation is

 

m=9j , Mr. Nelson is 9 times his son's age currently.

 

In 9 years, there is a new equation

 

m+9=3(j+9), Mr Nelson will be 3 times his son's age in 9 years.

 

Simplifying the second equation, gives:

 

m=3j+18

 

Subtract the two equations to eliminate m (it's easiest), gives:

 

0=6j-18

 

Solve for j to get

 

18=6j

 

3=j

 

The son is currently 3 years old, so Mr. Nelson who is 9 times his son's age currently is 27 years old, or,

 

m=9j=9*3=27