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.
Related Topics:
Examples of Algebra Age Problems that involves one person,
More Algebra Word Problems,
Algebra Worksheets,
Algebra Games
In these lessons, we will learn how to solve age problems that involve the ages of two or more people. In this case, using a table would be a good idea. A table will help you to organize the information and to write the equations. This is shown in the following age word problems that involve more than one person.
Example:
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as
old as Alice. How old is Peter now?
Solution:
Step 1: Set up a table.

age now 
age in 5 yrs 
John 


Peter 


Alice 


Step 2: Fill in the table with information given in the question.
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?
Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.

age now 
age in 5 yrs 
John 
2x 
2x + 5 
Peter 
x 
x + 5 
Alice 
x – 5 
x – 5 + 5 
Write the new relationship in an equation using the ages in 5 yrs.
In 5 years, John will be three times as old as Alice.
2x + 5 = 3(x – 5 + 5)
2x + 5 = 3x
Isolate variable x
x = 5
Answer: Peter is now 5 years old.
Example:
John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time,
the sum of their ages will be 58. How old is John now?
Solution:
Step 1: Set up a table.
age now 
age in 2 yrs 

John’s father 


John 


Alice 


Step 2: Fill in the table with information given in the question.
John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?
Let x be John’s age now. Add 2 to get the ages in 2 yrs.
age now 
age in 2 yrs 

John’s father 
5x 
5x + 2 
John 
x 
x + 2 
Alice 
Write the new relationship in an equation using the ages in 2 yrs.
In two years time, the sum of their ages will be 58.
Answer: John is now 8 years old.
The following videos show more examples of algebra age problems:
Example: Mary is 3 times as old as her son. In 12 years, Mary's age will be one year less than twice her son's age. Find their ages now.
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