The present age of Bart is 9 years old
Solution:
Let "x" be the present age of Tara
Let "y" be the present age of Bart
Given that today the sum of ages of Tara and Bart is 33
Therefore,
present age of Tara + present age of Bart = 33
x + y = 33 ---------- eqn 1
Six years from now Tara will be twice as old as Bart
Therefore,
Age of Tara after 6 years = x + 6
Age of Bart after 6 years = y + 6
Tara will be twice as old as Bart
Age of Tara after 6 years = 2(Age of Bart after 6 years)
x + 6 = 2( y + 6 )
x + 6 = 2y + 12
x - 2y = 12 - 6
x - 2y = 6 -------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 33 - y ------ eqn 3
Substitute eqn 3 in eqn 2
33 - y - 2y = 6
33 - 3y = 6
-3y = 6 - 33
-3y = -27
y = 9
From eqn 3,
x = 33 - 9
x = 24
Thus present age of Bart is 9 years old