Question

The product of a particular number and a second value, which is given by the sum of 8 and the original number, is 65. What is the number? A. x = 81 B. x = −13; x = 5 C. x = −9; x = 9 D. x = 5

Answer 1

Given:

The product of a particular number is 65.

Second value is given by the sum of 8 and the original number.

To find:

The unknown number.

Solution:

Let x be the unknown number.

Then, second number = x+8

The product of a particular number is 65.

$x\times (x+8)=65$

$x^2+8x=65$

$x^2+8x-65=0$

Splitting the middle term, we get

$x^2+13x-5x-65=0$

$x(x+13)-5(x+13)=0$

$(x-5)(x+13)=0$

Using zero product property, we get

$x-5=0$ and $x+13=0$

$x=5$ and $x=-13$

So, the unknown number is either 5 or -13.

Therefore, the correct option is B.