Question

The sum of the ages of father and his son is 35 and the product of their ages is 150 Find their ages .with Word problem​

Answer 1

✨Answer:

Son's age is 5 yrs and father age is 30 years.

✨Step-by-step explanation:

✔️Let sons age be x.

✔️Fathers age be y.

Sum of ages = 35 yrs

Product of ages = 150 yrs.

X + y = 35

Xy = 150

➡️Y = 35-x.

Xy = x(35-x)

Or,

x (35 - x) = 150

35x - x^2 = 150

Multiply by - 1 :

x^2 - 35x = - 150

x^2 - 35x + 150 = 0

X^2 - 30x - 5x + 150 = 0

x(x - 30) - 5 (x - 30) = 0

(x-5) (x - 30) = 0

x = 5 yrs or x = 30 yrs

When x = 5,

Sons age = 5 yrs

Fathers age = 35 - 5 = 30 yrs

When x = 30

Sons age = 30 yrs

Fathers age = 35 - 30 = 5 yrs

This is logically not possible.

Therefore, x = 5 yrs.

➡️ Son's age = 5 yrs

➡️ Father's age = 30 yrs.

Hence age of son is 5 years and age of father is 30 years.

Answer 2

AnswEr:

• Age of father = 30 years
• Age of son = 5 years

ExplanaTion:

Let -

• Age of father be x years.
• Age of son be y years.

According to the question,

• Sum of their ages is 35.
• Product of their ages is 150.

$\longrightarrow$ x + y = 35.....(1)

$\longrightarrow$ xy = 150.......(2)

From (1),

$\longrightarrow$ x = 35 - y

Put the value of x in (2).

$\longrightarrow$ ( 35 - y ) y = 150

$\longrightarrow$ 35y - y² = 150

$\longrightarrow$ y² - 35y + 150 = 0

Splitting middle term, we get,

$\longrightarrow$ y = 5 or 30

Rejecting y = 30, we get,

• Age of father will be 30 years
• Age of son will be years.