Question

sum of the present ages of two friends are 23 years, five years ago product of their ages was 42. find their ages 5 years hence​

Answer 1

Answer:

Their ages 5 year hence will be 16 and 17 years.

Step-by-step explanation:

Given :   sum of the present ages of two friends are 23 years

Let present age of one friend is x years

then present age of other friend is (23- x) years

Also given five years ago product of their ages was 42.

five year ago, age of one friend is (x - 5) years

and five year ago, age of other friend is (18 - x) years

thus,

$(x-5)\times (18-x)=42$

Apply distributive rule $\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$23x-x^2-90=42$

$-x^2+23x-132=0$

Simplify for x by factorizing ,

Using middle term splitting method,

23x can be written as -11x and -12x

$-x^2+11x+12x-132=0$

Taking -x common from first two term and -12x common from last two terms, we have,

$-x(x-11)+12(x-11)=0$

$(x-11)(-x+12)=0$

Thus, x = 11 and  x = 12

When x = 11 age of other friend will be 23 - 11 = 12

when x = 12 age of other friend will be 23 - 12 = 11

Thus, their ages 5 year hence will be 11 + 5 = 16 and 12 + 5 = 17

Thus, their ages 5 year hence will be 16 and 17 years.

Answer 2

Their ages 5 years hence​ 16 years, 17 years or 17 years, 16 years.

Step-by-step explanation:

Let the present ages of two friends = x and y

To find, their ages 5 years hence​ = ?

According to question,

x + y = 23

⇒ y = 23 - x    ....(1)

Also,

Five years ago,

The ages of two friends = (x - 5) and (y - 5)

(x - 5)(y - 5) = 42

Using (1), we get

⇒ (x - 5)(23 -x  - 5) = 42

⇒ (x - 5)(18 -x) = 42

⇒ $18x-x^{2} -90+5x=42$

⇒ $x^{2} -23x+132=0$

⇒ $x^{2} -12x-11x+132=0$

⇒ (x - 11)(x - 12) = 0

∴ x = 11, 12

Putting the value of x in equation (1), we get

11 + y = 23 ⇒y = 12

or 12 + y = 23 ⇒ y = 11

Hence,  their ages 5 years hence​ 16 years, 17 years or 17 years, 16 years.