What is the age of both father and son? | Algebra | Maths | Tutorial

QUESTION
The age of a father is twice the age of his son. Twenty years ago, his age was 6 times his son’s age. What is the age of both father and son?

SOLUTION

Step 1: Define

1. Let X = Age of Son

2. Therefore the age of the father is 2X (as he is twice the age of his son)

Step 2: Their Age 20 years ago

Their age 20 years ago

Father = 2X – 20

Son = X – 20

Step 3: Father is Six Times Sons Age

As the age of the father is 6 times the age of the son twenty years ago.

We illustrate this as:

6 * (Age of Son) = 6 * (X – 20) = Fathers age 20 years ago

Step 4: Solving for X (Sons Age)

As we know that 20 years ago the fathers age is 2X – 20 and also 6 * (X – 20) we can solve this simultaneous equation.

2X – 20 = 6 * (X – 20)

2X – 20 = 6X – 120

-20 + 120 = 6X – 2X

100 = 4X

X = 25 (The sons age is therefore 25)

Step 5: Calculating Fathers Age

The fathers age is 2X = 2 * 25 = 50

Step 6: Verification

To make sure that this is correct we can check to see what their ages were 20 years ago and confirm if the father really was 6 times older than the son.

Father = (2X – 20) = 2(25) – 20 = 30

Son = (X – 20) = 25 – 20 = 5

5 * 6 = 30 (Confirmation that the solution is correct!)