Question

A girl is 6 years younger than her brother. The product of their ages is 135.find their ages

Answer 1

Answer:

The girl's age = 9

The brother's age = 15

Step-by-step explanation:

Let the brother's age be x. So, the sister's age is X-6 .

therefore,

x × (x-6)= 135

x^2-6x=135

x^2 -6x - 135=0

using middle term break

(x+9)(x−15)=0

so,

either X+9 =0. X=-9 (NA because age cannot be negative)

or X-15=0 X=15

The brother is 15 years old, so the sister has to be (15-6) = 9

Answer 2

Required Answer :

The age of girl is 9 years and her brother's age is 15 years

Given :

• A girl is 6 years younger than her brother.
• Product of the ages of girl and her brother = 135

To find :

• The present age of the girl and her brother = ?

Solution :

Let the age of brother = x years

→ Girl's age = x - 6 years

→ Age of brother × Age of girl = 135

→ x(x - 6) = 135

→ x² - 6x = 135

→ x² - 6x - 135 = 0

A quadratic equation is formed. To split the quadratic equation into the middle term, we need two numbers such that their product is - 135x² and difference is - 6x

→ x² - 15x + 9x - 135 = 0

→ x(x - 15) + 9(x - 15) = 0

→ (x + 9)(x - 15) = 0

→ x = - 9 or x = 15

As we know, the age cannot be negative. So, - 9 will be rejected.

→ The value of x = 15

Substituting the value of x :

Age of girl :

→ x - 6

→ 15 - 6

= 9 years

Age of brother :

→ x = 15 years

Therefore, the age of girl is 9 years and her brother's age is 15 years