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.

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.

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.