Tom's and tim's ages add up to 21 years. in 3 years tom's will be twice tim's age how old are they now?

Tom's age = a
Tim's age = b

We know that
a + b = 21                 (Tom's and Tim's ages add up to 21 years)
a + 3 = 2b                 (In 3 years, Tom's age will be twice Tim's age)

Let's solve this set of equations using algebra.
First, we want to find a in terms of b. We can do this easily with our first eqn.
a + b = 21
Subtract b from each side. (subtraction property of equality)
a = 21 - b

Then, substitute 21 - b for a in our second equation.
21 - b + 3 = 2b

Now that we have only one variable in our eqn, we can solve it easily.

Add the 21 and 3.
24 - b = 2b
Add b to each side to get rid of the -b. (add. prop. of eq)
24 = 3b
Divide each side by 3. (div. prop. of eq)
8 = b

Now that we know that b = 8, we can use this in an earlier equation to find a.
a + b = 21
a + 8 = 21
Subtract 8 from each side.
a = 13

Final  Tom is 13 and Tim is 8.