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Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.?
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Mrs Tendon has two sons, one being exactly one year older than the oth...
Given Information:
Mrs. Tendon has two sons, one being exactly one year older than the other.
Her age at present is equal to the sum of the squares of the ages of her sons.
4 years hence her age becomes five times the age of the elder son.
Let's solve the problem step by step:
Step 1: Set up the equations
Let's assume the age of the younger son is x years.
Then, the age of the elder son would be (x + 1) years.
According to the given information:
1. Mrs. Tendon's age = sum of the squares of the ages of her sons
So, Mrs. Tendon's age = x^2 + (x + 1)^2
2. 4 years hence, Mrs. Tendon's age = 5 * (age of the elder son)
So, (x^2 + (x + 1)^2) + 4 = 5 * (x + 1)
Step 2: Solve the equations
Expanding the equations, we get:
1. x^2 + x^2 + 2x + 1 = x^2 + x^2 + 2x + 1
2x^2 + 2x + 1 = 2x^2 + 2x + 1
2. x^2 + (x + 1)^2 + 4 = 5x + 5
x^2 + (x^2 + 2x + 1) + 4 = 5x + 5
2x^2 + 2x + 5 = 5x + 5
2x^2 - 3x = 0
x(2x - 3) = 0
x = 0 or x = 3/2
Since age cannot be zero, the younger son's age (x) is 3/2 = 1.5 years.
Step 3: Calculate the ages of the sons
Younger son's age = 1.5 years
Elder son's age = 1.5 + 1 = 2.5 years
Therefore, the present ages of Mrs. Tendon's sons are:
Younger son: 1.5 years
Elder son: 2.5 years
Mrs. Tendon has two sons, one being exactly one year older than the other.
Her age at present is equal to the sum of the squares of the ages of her sons.
4 years hence her age becomes five times the age of the elder son.
Let's solve the problem step by step:
Step 1: Set up the equations
Let's assume the age of the younger son is x years.
Then, the age of the elder son would be (x + 1) years.
According to the given information:
1. Mrs. Tendon's age = sum of the squares of the ages of her sons
So, Mrs. Tendon's age = x^2 + (x + 1)^2
2. 4 years hence, Mrs. Tendon's age = 5 * (age of the elder son)
So, (x^2 + (x + 1)^2) + 4 = 5 * (x + 1)
Step 2: Solve the equations
Expanding the equations, we get:
1. x^2 + x^2 + 2x + 1 = x^2 + x^2 + 2x + 1
2x^2 + 2x + 1 = 2x^2 + 2x + 1
2. x^2 + (x + 1)^2 + 4 = 5x + 5
x^2 + (x^2 + 2x + 1) + 4 = 5x + 5
2x^2 + 2x + 5 = 5x + 5
2x^2 - 3x = 0
x(2x - 3) = 0
x = 0 or x = 3/2
Since age cannot be zero, the younger son's age (x) is 3/2 = 1.5 years.
Step 3: Calculate the ages of the sons
Younger son's age = 1.5 years
Elder son's age = 1.5 + 1 = 2.5 years
Therefore, the present ages of Mrs. Tendon's sons are:
Younger son: 1.5 years
Elder son: 2.5 years
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Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.?
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Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? 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 Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.?.
Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? 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 Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.?.
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Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.?, a detailed solution for Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? has been provided alongside types of Mrs Tendon has two sons, one being exactly one year older than the other. At present, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the present ages of her sons.? theory, EduRev gives you an
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