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Father's age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Question

Father's age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

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Solution

Let's denote:

F = Father's current age C1 = First child's current age C2 = Second child's current age

From the problem, we have two equations:

  1. F = 3 * (C1 + C2) (Father's age is three times the sum of ages of his two children)

  2. F + 5 = 2 * ((C1 + 5) + (C2 + 5)) (After 5 years his age will be twice the sum of ages of two children)

We can simplify the second equation to:

  1. F + 5 = 2 * (C1 + C2 + 10)

Substitute the first equation (F = 3 * (C1 + C2)) into the second equation:

3 * (C1 + C2) + 5 = 2 * (C1 + C2 + 10)

Solving this equation gives:

C1 + C2 = 15

Substitute C1 + C2 = 15 into the first equation:

F = 3 * 15 = 45

So, the father is 45 years old.

This problem has been solved

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