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The age of father is twice the sum of the ages of his two children . After 20 years his age will be equal to the sum of the ages of his children . Find the age of the father ?
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Problem: Find the age of the father if his age is twice the sum of his children's ages and after 20 years, his age will be equal to the sum of his children's ages.
Solution:
Let the age of the father be "F" and the ages of his two children be "C1" and "C2".
1. Translate the problem into an equation:
- The age of the father is twice the sum of his children's ages: F = 2(C1 + C2)
- After 20 years, his age will be equal to the sum of his children's ages: F + 20 = C1 + 20 + C2 + 20
2. Simplify the equations:
- F = 2C1 + 2C2
- F = C1 + C2 + 40
3. Set the two equations equal to each other:
- 2C1 + 2C2 = C1 + C2 + 40
- C1 + C2 = 40
4. Use this equation to solve for one variable in terms of the other:
- C1 = 40 - C2
5. Substitute this expression for C1 into one of the original equations:
- F = 2(40 - C2) + 2C2
- F = 80 - C2
6. Substitute this expression for F into the other original equation:
- 80 - C2 + 20 = (40 - C2) + (C2 + 20)
- 100 - C2 = 60
- C2 = 40
7. Use this value to solve for the other variable:
- C1 = 40 - C2 = 0
8. Check the answer:
- F = 80 - C2 = 80 - 40 = 40
- After 20 years, the father will be 60 and his children will be 20 and 20, which adds up to 60.
Answer: The age of the father is 40.
Solution:
Let the age of the father be "F" and the ages of his two children be "C1" and "C2".
1. Translate the problem into an equation:
- The age of the father is twice the sum of his children's ages: F = 2(C1 + C2)
- After 20 years, his age will be equal to the sum of his children's ages: F + 20 = C1 + 20 + C2 + 20
2. Simplify the equations:
- F = 2C1 + 2C2
- F = C1 + C2 + 40
3. Set the two equations equal to each other:
- 2C1 + 2C2 = C1 + C2 + 40
- C1 + C2 = 40
4. Use this equation to solve for one variable in terms of the other:
- C1 = 40 - C2
5. Substitute this expression for C1 into one of the original equations:
- F = 2(40 - C2) + 2C2
- F = 80 - C2
6. Substitute this expression for F into the other original equation:
- 80 - C2 + 20 = (40 - C2) + (C2 + 20)
- 100 - C2 = 60
- C2 = 40
7. Use this value to solve for the other variable:
- C1 = 40 - C2 = 0
8. Check the answer:
- F = 80 - C2 = 80 - 40 = 40
- After 20 years, the father will be 60 and his children will be 20 and 20, which adds up to 60.
Answer: The age of the father is 40.
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