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 answer: Tom is 13 and Tim is 8.