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!)
Fine! You’re smarter than me. Happy?
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Check your formulas in the confirmation. 2(50)-20 does not =30.
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Thank you, corrected typo!
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