Age Word Problems

Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future.

If the problem involves a single person, then it is similar to an Integer Problem. Read the problem carefully to determine the relationship between the numbers. If the age problem involves the ages of two or more people then using a table would be a good idea.


Jack’s father is 45. He is 15 years older than twice Jack’s age. How old is Jack?
We can begin by assigning a variable to what we’re asked to find. Here this is Jack’s age, so let Jack’s age = x.
We also know from the information given in the problem that 45 is 15 more than twice Jack’s age. How can we translate this from words into mathematical symbols? What is twice Jack’s age?

Well, Jack’s age is x, so twice Jack’s age is 2x, and 15 more than twice Jack’s age is 15 + 2x. That equals 45, right? Now we have an equation in terms of one variable that we can solve for x : 45 = 15 + 2x.

Original statement of the problem : 45 = 15 + 2x
Subtract 15 from each side : 30 = 2x
Divide both sides by 2 : 15 = x
Since x is Jack’s age and x = 15, this means that Jack is 15 years old.

It’s always a good idea to check our answer:
Twice Jack’s age is 2 x 15 : 30
15 more than 30 is 15 + 30 : 45
This should be the age of Jack’s father, and it is.


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