Algebra Age 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 following age word problem that involves more than one person.

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.

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.

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.

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.

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 foillowing videos show more examples of algebra age problems:

Custom Search