# In eight years, Jack will be 2/3 as old as Tom. Four years ago he was 1/3 as old as Tom. Find their present ages.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

In eight years, Jack will be 2/3 as old as Tom. Four years ago he was 1/3 as old as Tom. Let the age of Jack be J and that of Tom be T.

According to the data provided

J + 8 = (2/3)*(T + 8) and J - 4 = (1/3)*(T - 4)

=> 3J + 24 = 2T + 16 and 3J - 12 = T - 4

Subtracting the two equations gives

T + 20 = 36

=> T = 16

and J = 8

Presently Jack is 8 and Tom is 16.

leedygood7 | High School Teacher | (Level 2) eNoter

Posted on

Let Jack's present age be x and Tom's present age be y

If we write the condition given in the question to equations,

x+8 = 2/3(y+8)
x-4 = 1/3(y-4)

In the first equation,
3x+24 = 2y+16
=> y = 3/2x + 4

Then we can plug in the equation of y into the second equation
x-4 = 1/3(3/2x+4-4) = 1/2x

Therefore, solving the last equation, x-4 = 1/2x,

x = 8
y = 3/2*8 +4 = 16

Jack's present age is 8, Tom's present age is 16