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10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all?
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10 years ago the sum of the ages of two sons was one third of their fa...
To solve the problem, let’s define the variables and analyze the information step by step.
Define Variables
- Let the present age of the younger son be x.
- Then, the age of the older son is x + 2.
- Let the father's present age be y.
Information from 10 Years Ago
- Ten years ago, the younger son’s age was x - 10 and the older son’s age was (x + 2) - 10 = x - 8.
- The sum of their ages at that time was:
- (x - 10) + (x - 8) = 2x - 18.
- According to the problem, this sum was one third of the father's age 10 years ago:
- y - 10.
Therefore, we have the equation:
Equation 1:
2x - 18 = (y - 10) / 3
Multiplying through by 3 gives:
6x - 54 = y - 10
So,
Equation 2:
y = 6x - 44
Current Age Relationships
- The sum of the present ages of the two sons is:
- x + (x + 2) = 2x + 2.
- According to the problem, this sum is 14 years less than the father’s present age:
Equation 3:
2x + 2 = y - 14
Rearranging gives:
y = 2x + 16
Solving the Equations
- Now, set the right-hand sides of Equations 2 and 3 equal to each other:
6x - 44 = 2x + 16
Simplifying gives:
4x = 60
x = 15
- So, the younger son's age is 15 years, and the older son is 17 years (15 + 2).
Finding Father's Age
- Substitute x back into Equation 2 to find the father’s age:
y = 6(15) - 44 = 90 - 44 = 46
Final Ages
- Younger Son: 15 years
- Older Son: 17 years
- Father: 46 years
This structured approach provides clarity in solving age-related problems!
Define Variables
- Let the present age of the younger son be x.
- Then, the age of the older son is x + 2.
- Let the father's present age be y.
Information from 10 Years Ago
- Ten years ago, the younger son’s age was x - 10 and the older son’s age was (x + 2) - 10 = x - 8.
- The sum of their ages at that time was:
- (x - 10) + (x - 8) = 2x - 18.
- According to the problem, this sum was one third of the father's age 10 years ago:
- y - 10.
Therefore, we have the equation:
Equation 1:
2x - 18 = (y - 10) / 3
Multiplying through by 3 gives:
6x - 54 = y - 10
So,
Equation 2:
y = 6x - 44
Current Age Relationships
- The sum of the present ages of the two sons is:
- x + (x + 2) = 2x + 2.
- According to the problem, this sum is 14 years less than the father’s present age:
Equation 3:
2x + 2 = y - 14
Rearranging gives:
y = 2x + 16
Solving the Equations
- Now, set the right-hand sides of Equations 2 and 3 equal to each other:
6x - 44 = 2x + 16
Simplifying gives:
4x = 60
x = 15
- So, the younger son's age is 15 years, and the older son is 17 years (15 + 2).
Finding Father's Age
- Substitute x back into Equation 2 to find the father’s age:
y = 6(15) - 44 = 90 - 44 = 46
Final Ages
- Younger Son: 15 years
- Older Son: 17 years
- Father: 46 years
This structured approach provides clarity in solving age-related problems!
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10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all?
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10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all?.
10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 10 years ago the sum of the ages of two sons was one third of their father's age the sum of the present ages of two sons is 14 years less than the father's present age if one son is 2 years older than the other find the present ages of all?.
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