Answer:
Here, K represents the current age of Katie and T represents the current age of Thomas.
(a)
As per the statement:
Katie is currently twice the age of Thomas.
⇒
......[1]
It is also given that in 6 years Katie will be 4 times Thomas's current age.


Subtract 6 from both sides we get;
......[2]
A system of equations that describe the situation is:


(b)
To find the solution:
equate [1] and [2] we have;

Subtract 2T from both sides we have;

Add 6 to both sides we get;

Divide both sides by 2 we have;
T = 3 years
Substitute this in equation [1] we get;
K = 2(3) = 6 years.
Therefore, the current age of Katie and Thomas are 6 years and 3 years.