The age of the father is twice the sum of the ages of his two children. After 20years, his age will be equal to the sum of the ages of his children. Find the age ofthe father
Question
The age of the father is twice the sum of the ages of his two children. After 20years, his age will be equal to the sum of the ages of his children. Find the age ofthe father
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:
- F = 2*(C1 + C2) (The father's age is twice the sum of the ages of his two children)
- F + 20 = (C1 + 20) + (C2 + 20) (In 20 years, the father's age will be equal to the sum of the ages of his children)
We can simplify the second equation to:
- F + 20 = C1 + C2 + 40
- F = C1 + C2 + 20
Now we have two equations with the same left side (F), so we can set the right sides equal to each other:
2*(C1 + C2) = C1 + C2 + 20
Solving this equation will give us the sum of the children's ages. Then we can substitute this value into either of the original equations to find the father's age.
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