## Age Problems

Here are some examples for calculating age in word problems.

##### Example 1

Phil is Tom's father. Phil is 35 years old. Three years ago, Phil was four times as old as his son was then. How old is Tom now?

First, circle what it is you must ultimately find— how old is Tom now? Therefore, let t be Tom's age now. Then three years ago, Tom's age would be t – 3. Four times Tom's age three years ago would be 4( t – 3). Phil's age three years ago would be 35 – 3 = 32. A simple chart may also be helpful.

now 3 years ago
Phil 35 32
Tom t t-3

Now, use the problem to set up an equation. Therefore, Tom is now 11.

##### Example 2

Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa?

First, circle what you must find— how old is Lisa? Let Lisa equal x. Therefore, Kathy is x + 16. (Note that since Lisa is 16 years younger than Kathy, you must add 16 years to Lisa to denote Kathy's age.) Now, use the problem to set up an equation. Therefore, Lisa is 7 years old.
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