Algebra: Age Word Problems

Printable & Online Algebra Worksheets

How To Solve Age Word Problems?

Age word problems often require you to set up and solve algebraic equations to find unknown ages. These problems typically involve:
Present ages: The current ages of the people involved.
Past ages: Ages of the people at some point in the past (e.g., “5 years ago”).
Future ages: Ages of the people at some point in the future (e.g., “in 10 years”).
Relationships between ages: These are the key pieces of information. They might be stated as:
“X is twice as old as Y."
“X is 5 years older than Y."
“In 10 years, X will be three times as old as Y."

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 current age. Look at the question and put the relevant expressions above it.

 

Step 2: Write out the equation.

 

Isolate variable x

 

Answer: John is now 18 years old.

How To Use Algebra To Solve Age Problems?

Examples:

1. Ten years from now, Orlando will be three times older than he is today. What is his current age?
2. In 20 years, Kayleen will be four times older than she is today. What is her current age?

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How To Solve Age Problems Involving More Than One Person?

Using tables to solve age word problems that involves two or more persons with tables can help you organize the information clearly, which makes it much easier to set up the correct equations. The table acts as a visual guide to translate the problem’s text into mathematical expressions.

The following diagram shows how to solve an age word problem involving two people using a table. Scroll down the page for more examples and solutions.

 

Algebra Worksheets
Practice your skills with the following worksheets:
Printable & Online Algebra Worksheets

1. Set Up the Table
The table should have three columns and a row for each person in the problem.
Rows: One for each person.
“Person”: The names of the people.
“Current Age”: The algebraic expression for each person’s current age.
“Other Time Period”: A column for any other time mentioned in the problem.
2. Fill in the “Current Age” Column
Choose a variable (like x) for one person’s age and express the others’ ages in terms of that variable, based on the information given in the problem.
3. Fill in the “Other Time Period” Column
Use simple addition or subtraction to express each person’s age in the specified time period.
To represent a future age, add the number of years to the current age expression.
To represent a past age, subtract the number of years from the current age expression.
4. Use the Table to Form an Equation
The problem will contain a key phrase that relates the ages in one of the columns. Use the expressions from your table to build a single equation.
5. Solve and Check
Solve the equation for your variable. Then, use that value to find the ages of everyone in the problem and check that your solution works with all the conditions in the original word problem.

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.

	current age	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 current age. Add 5 to get the ages in 5 yrs.

	current age	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.

	current age	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 current age. Add 2 to get the ages in 2 yrs.

	current age	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?

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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?

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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?

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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:

1. Sally is 3 times as old as John. 8 years from now, Sally will be twice as old as John. How old is John?
2. 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?
3. 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?
4. 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?
5. 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?
6. 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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Check out many other Algebra Word Problems
Age Word Problems, Average Word Problems, Coin Word Problems, Consecutive Integer Word Problems, Digit Word Problems, Distance Word Problems, Fraction Word Problems, Geometry Word Problems, Integer Word Problems, Interest Word Problems, Lever Word Problems, Mixture Word Problems, Money Word Problems, Motion & Distance Word Problems, Number Sequence Word Problems, Proportion Word Problems, Quadratic Equation Word Problems, Ratio Word Problems, Symbol Word Problems, Variation Word Problems, Work Word Problems.

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