Algebra: Age Word Problems
Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future.
Related Pages
Word Problems Involving Age
Solving Age Word Problems Using Algebra
More Algebra Lessons
How To Solve Age Word Problems?
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. This is shown in the examples involving a single person.
If the age problem involves the ages of two or more people then 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 examples involving more than one person.
How To Solve Age Problems Involving A Single Person?
Example:
Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?
Solution:
Step 1: Let x be John’s age now. Look at the question and
put the relevant expressions above it.
Step 2: Write out the equation.
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Isolate variable x
Answer: John is now 18 years old.
How To Use Algebra To Solve Age Problems?
Examples:
- Ten years from now, Orlando will be three times older than he is today. What is his current age?
- In 20 years, Kayleen will be four times older than she is today. What is her current age?
How To Solve Age Problems Involving 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.
How To Solve Word Problems With Multiple Ages?
Example:
Ben is eight years older than Sarah. 10 years ago, Ben was twice as old as Sarah. Currently, how old is
Ben and Sarah?
Algebra Word Problems With Multiple Ages
Example:
Mary is three times as old as her son. In 12 years, Mary’s age will be one year less than twice her
son’s age. How old is each now?
Algebra Word Problem With Past And Present Ages
Example:
Arun is 4 times as old as Anusha is today. Sixty years ago, Arun was 6 times as old as Anusha.
How old are they today?
Algebra Age Word Problem With Past, Present, And Future Ages
How to organize the data using a table and solve using a system of linear equations?
Examples:
- Sally is 3 times as old as John. 8 years from now, Sally will be twice as old as John. How old is John?
- Kim is 6 years more than twice Timothy’s age. 2 years ago, Kim was three times as old as Timothy. How old was Kim 2 years ago?
- Leah is 2 less than 3 times Rachel’s age. 3 years from now, Leah will be 7 more than twice Rachel’s age. How old will Rachel be in 3 years from now?
- Becca is twice as old as Susan and Greg is 9 years older than Susan. 3 years ago, Becca was 9 less than 3 times Susan’s age. How old is Greg now?
- Lauren is 3 less than twice Andrew’s age. 4 years from now, Sam will be 2 more than twice Andrew’s age. 5 years ago, Sam was three times Andrew’s age. How old was Lauren 5 years ago?
- Gabby is 1 year more than twice Larry’s age. 3 years from now, Megan will be 27 less than twice Gabby’s age. 4 years ago, Megan was 1 year less than 3 times Larry’s age. How old will Megan be 3 years from now?
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