Mrs. Tendon has two sons, one being exactly one year old than the other. Her age is equal to the sum of the squares of her two sons. In 4 years, her age will be 5 times the age of the eldest son. Find the age of her sons.
Answers
Step-by-step explanation:
Let , the age of elder son be "x".
Then the age younger son = x -1.
given that,
Tendon 's age is equal to the sum of
squares of her two son's.
So, tendon 's age = (x)² +(x - 1)²
= x² + x² + 1² - 2x
Tendon 's age = (2x² - 2x + 1 .) years.-- eq-(1)
And also given that, in 4 years her age will be 5 times the age of the eldest son.
After 4 years , Elder son's age = x + 4.
Tendon's age = 5(x + 4)
Tendon's age = (5x + 20) years.-- eq-(2)
From eq -(1) ,
Tendon's age after 4 years = (2x² - 2x +1 ) + 4
Tendon's age = 2x²- 2x +5 -- eq- (3)
Equate eq (2) & (3).
5x + 20 = 2x² - 2x + 5
2x² - 2x +5 - 5x - 20 = 0
2x² - 7x - 15 = 0
2x² - 10x + 3x - 15 = 0
2x ( x - 5) + 3(x - 5) = 0
(2x + 3)(x - 5) = 0
2x + 3 = 0
2x = -3
x = -3/2.
x - 5 = 0
x = 5.
Age of a person cannot be negative so Positive value is taken.
Hence, x = 5.
Therefore, Age of elder son = x = 5 years and age of younger son = (x - 1) = (5-1) = 4 years.
Answer:
Let , the age of elder son be "x".
Then the age younger son = x -1.
given that,
Tendon 's age is equal to the sum of
squares of her two son's.
So, tendon 's age = (x)² +(x - 1)²
= x² + x² + 1² - 2x
Tendon 's age = (2x² - 2x + 1 .) years.-- eq-(1)
And also given that, in 4 years her age will be 5 times the age of the eldest son.
After 4 years , Elder son's age = x + 4.
Tendon's age = 5(x + 4)
Tendon's age = (5x + 20) years.-- eq-(2)
From eq -(1) ,
Tendon's age after 4 years = (2x² - 2x +1 ) + 4
Tendon's age = 2x²- 2x +5 -- eq- (3)
Equate eq (2) & (3).
5x + 20 = 2x² - 2x + 5
2x² - 2x +5 - 5x - 20 = 0
2x² - 7x - 15 = 0
2x² - 10x + 3x - 15 = 0
2x ( x - 5) + 3(x - 5) = 0
(2x + 3)(x - 5) = 0
2x + 3 = 0
2x = -3
x = -3/2.
x - 5 = 0
x = 5.
Age of a person cannot be negative so Positive value is taken.
Hence, x = 5.
Therefore, Age of elder son = x = 5 years and age of younger son = (x - 1) = (5-1) = 4 years.
Step-by-step explanation: