Question

. The product of Shabnam's age 5 years ago, with her age 9 years later is 176. Find present age of shabnam.

Answer 1

Step-by-step explanation:

Assume that the present age of Shabnam is x years.

The product of Shabnam's age 5 years ago, with her age 9 years later is 176.

• 5 years ago, age of Shabnam = (x - 5) years
• 9 years later, age of Shabnam = (x + 9) years

As per given condition,

→ (x - 5)(x + 9) = 176

→ x(y + 9) -5(x + 9) = 176

→ x² + 9x - 5x - 45 = 176

→ x² + 9x - 5x = 221

→ x² + 4x - 221 = 0

Split the middle term

→ x² + 17x - 13x - 221 = 0

→ x(x + 17) -13(x + 17) = 0

→ (x - 13) (x + 17) = 0

On comparing we get,

→ x = 13, -17

Age can't be negative. So, negative one neglected.

Hence, the present age of the Shabnam is 13 years.

Answer 2

✬ Present Age = 13 Years ✬

Step-by-step explanation:

Given:

• The product of Shabnam's age 5 years ago with her age 9 years later is 176.

To Find:

• What is the present age of Shabnam ?

Solution: Let the present age of Shabnam be x years. Therefore,

➟ Her age 5 years ago = (x – 5) years....(1)

➟ Her age 9 years later = (x + 9) years....(2)

A/q

• Equation 1 $\times$ Equation 2 = 176

$\implies{\rm }$ (x – 5) (x + 9) = 176

$\implies{\rm }$ x(x + 9) – 5(x + 9) = 176

$\implies{\rm }$ x² + 9x – 5x – 45 = 176

$\implies{\rm }$ x² + 4x = 176 + 45

$\implies{\rm }$ x² + 4x = 221

$\implies{\rm }$ x² + 4x – 221

Now, solving this equation by middle term splitting method.

➭ x² + 4x – 221

➭ x² + 17x – 13x – 221

➭ x (x + 17) – 13 (x + 17)

➭ (x + 17) (x – 13)

➭ x + 17 = 0 or x – 13 = 0➭ x = –17 or x = 13

[ Age cannot be negative so we will take the positive value of x ]

Hence, Present age of Shabnam is 13 years.