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.
