Question

The sum of ages (in years) of a son and his father is 35
years and product of their ages is 150 years, find their ages.​

Answer 1

ANSWER:

• Age of son = 5

• Age of father = 30

GIVEN:

• The sum of ages of son and his father is 35 years and product of their ages is 150 years.

TO FIND:

• Age of son and age of father.

EXPLANATION:

Let the age of son be x and the age father be y

=> x + y = 35

=> x = 35 - y

=> xy = 150

Substitute x = 35 - y

=> (35 - y)y = 150

=> 35y - y² = 150

=> y² - 35y + 150 = 0

Splitting the middle term

=> y² - 30y - 5y + 150 = 0

=> y(y - 30) - 5(y - 30) = 0

=> (y - 30)(y - 5) = 0

=> y = 30, y = 5

Father's age > Son's age

=> y > x

Therefore, y = 30

=> x + y = 35

Substitute y = 30

=> x + 30 = 35

=> x = 5

Age of son = 5

Age of father = 30

VERIFICATION:

=> xy = 150

Substitute x = 5, y = 30

=> 5(30) = 150

=> 150 = 150

HENCE VERIFIED.