**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!)

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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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