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.

Step 2: Write out the equation.

Isolate variable x

Answer: John is now 18 years old.

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

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.

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