Mrs tendon has two sons, one being exactly one year older than the other. at percentage, 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 percent ages of her sons. equation
Answers
2nd son = ( x + 1 ) years
ATQ
Mother's age = x^2 + ( x + 1 )^2
4 years later
5( x + 1 + 4 ) = x^2 + ( x + 1 )^2 + 4
5x + 25 = x^2 + x^2 + 2x + 1 + 5
5x + 25 = 2x^2 + 2x + 5
2x^2 - 3x - 20 = 0
Solve the equation and u can find their ages .
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: