Tara and bart are cousins. today, the sum of their ages is 33. six years from now tara will be twice as old as bart. how old is bart today

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

From eqn 3,

x = 33 - 9

Thus present age of Bart is 9 years old

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