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Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son?
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Problem: Two years ago father was 5 times as old as his son. 2 years later his age will be 8 years more than three times the age of the son. Find the present age of father and son.
Step 1: Assign Variables
Let x be the son's present age.
Let y be the father's present age.
Step 2: Translate the Sentences into Equations
Two years ago, father was 5 times as old as his son.
(y - 2) = 5(x - 2)
2 years later his age will be 8 years more than three times the age of the son.
(y + 2) = 3(x + 2) + 8
Step 3: Solve the Equations Simultaneously
Solve the system of equations to find the values of x and y.
(y - 2) = 5(x - 2)
(y - 2) = 5x - 10
y = 5x - 8
(y + 2) = 3(x + 2) + 8
y + 2 = 3x + 6 + 8
y = 3x + 12
Substitute y = 5x - 8 into y = 3x + 12
5x - 8 = 3x + 12
2x = 20
x = 10
Substitute x = 10 into y = 5x - 8
y = 5(10) - 8
y = 42
Step 4: Check the Solution
Check if the ages satisfy the given conditions.
Two years ago, father was 5 times as old as his son.
(y - 2) = 5(x - 2)
(42 - 2) = 5(10 - 2)
40 = 40 (True)
2 years later his age will be 8 years more than three times the age of the son.
(y + 2) = 3(x + 2) + 8
(42 + 2) = 3(10 + 2) + 8
44 = 44 (True)
Step 5: Conclusion
The present age of the father is 42 and the present age of the son is 10.
Step 1: Assign Variables
Let x be the son's present age.
Let y be the father's present age.
Step 2: Translate the Sentences into Equations
Two years ago, father was 5 times as old as his son.
(y - 2) = 5(x - 2)
2 years later his age will be 8 years more than three times the age of the son.
(y + 2) = 3(x + 2) + 8
Step 3: Solve the Equations Simultaneously
Solve the system of equations to find the values of x and y.
(y - 2) = 5(x - 2)
(y - 2) = 5x - 10
y = 5x - 8
(y + 2) = 3(x + 2) + 8
y + 2 = 3x + 6 + 8
y = 3x + 12
Substitute y = 5x - 8 into y = 3x + 12
5x - 8 = 3x + 12
2x = 20
x = 10
Substitute x = 10 into y = 5x - 8
y = 5(10) - 8
y = 42
Step 4: Check the Solution
Check if the ages satisfy the given conditions.
Two years ago, father was 5 times as old as his son.
(y - 2) = 5(x - 2)
(42 - 2) = 5(10 - 2)
40 = 40 (True)
2 years later his age will be 8 years more than three times the age of the son.
(y + 2) = 3(x + 2) + 8
(42 + 2) = 3(10 + 2) + 8
44 = 44 (True)
Step 5: Conclusion
The present age of the father is 42 and the present age of the son is 10.
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Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son?
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Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son? 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 Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son?.
Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son? 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 Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two years ago father was 5 times as old as his son 2 years later his age will be 8 years more than three times the age of the son find the present age of father and son?.
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