1. What are Age Problems?
Age problems are typically algebraic word problems, where in general the ages of two different people, both in the past and in the future are compared. The objective of age problems is usually to find each person’s current age. These problems are solved by forming and solving linear equations. Look at the age problem example shown below:
Example: Four years ago, Laura’s age was four times her sister’s current age. If her sister is currently 4 years old, work out Laura's current age.
In the above age problem, the ages of Laura and her sister are compared four years ago. The objective of this problem is to work out Laura’s current age using the given information and comparison in the question. This might seem trickier to work out, but can easily be done by using algebra and forming the equation. Let us now look at the three simple steps in order to solve these problems.
1.1 Simple steps to solve Age Problems
- Assume the person’s current age as a variable ‘x’.
- Using the information of ages in the past/future in the question, form an expression in terms of ‘x’.
For example: If a person’s current age is x:
His age after two years is x + 2.
His age before two years is x - 2.
- Form a linear equation using the comparisons of ages given in the question and solve it for x.
Let us now use the above-mentioned steps to solve the previous example.
Four years ago, Laura’s age was four times her sister’s current age. If her sister is currently 4 years old, work out Laura's current age.
Solution:
Step 1 - Assume Laura’s current age as ‘x’.
Step 2 - Forming an expression:
Laura’s age four years ago is ‘x - 4’.
Step 3 - Forming an equation:
Four times Laura’s sister’s current age is 4 × 4.
So, x - 4 = 4 × 4
Solving the above equation,
x - 4 = 16
x = 16 + 4 = 20
Hence Laura’s current age is 20 years.
1.2 Examples of Age Problems
Example 1: Jake is now twice his cousin's age. In 4 years' time, Jake will be 20. How old will his cousin be then?
Solution:
Step 1 - Assume Jake’s cousin’s current age as ‘x’.
Step 2 - Forming an expression:
Jake’s current age is ‘2x’.
Four years from now, Jake’s cousin’s age will be x + 4
and Jake’s age will be 2x + 4.
Step 3 - Forming an equation:
2x + 4 = 20
Solving the above equation,
2x = 20 - 4 = 16
x = 16 ÷ 2 = 8
Jake’s cousin four years from now will be 8 + 4 = 12 years.
Example 2: Jully is 3 years older than Ryan. The sum of their ages is 67. How old is Jully?
Step 1 - Assume Jully’s current age as ‘x’.
Step 2 - Forming an expression:
Ryan’s current age is ‘x - 3’.
Step 3 - Forming an equation:
x + (x - 3) = 89
Solving the above equation,
2x - 3 = 67
2x = 67 + 3 = 70
x = 79 ÷ 2 = 35
Hence, Jully is 35 years old.
