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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.

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 example 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.

Related Topics: More Algebra Word Problems

Age Problems Involving A Single Person

Example 1:

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.

example 1

Step 2: Write out the equation.

equations step 2

Isolate variable x

equations

Answer: John is now 18 years old.

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?


 



Age Problems Involving More Than One Person

Example 2:

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 3:

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

1/2 x

1/2 x + 2

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.

equations 3

Answer: John is now 8 years old.


 



Ben is eight years older than Sarah, 10 years ago. Ben is twice as old as Sarah. Currently, how old is Ban and Sarah?

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?

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?


 



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