Question

If fifteen less than two times a number is divided by six more than the number, the result is four less than 9 times the reciprocal of the number. Find the number

Answer 1

3

Explanation:

Given:

If fifteen less than two times a number is divided by six more than the number, the result is four less than 9 times the reciprocal of the number.

Question asked:

Find the number ?

Solution:

Let the number be
`x`

As given that:-

15 less than 2 times a number
`/` 6 more than the number = 4 less than 9 times the reciprocal of the number

Then the equation will be:-

`(2x-15)/(6+x) =9*(1)/(x) -4\\\\ (2x-15)/(6+x) =(9)/(x) -4\\\\ (2x-15)/(6+x) =(9-4x)/(x) \\ \\`

By cross multiplication:-

`x(2x-15)=(6+x)(9-4x)\\2x^(2) -15x=6(9-4x)+x(9-4x)\\2x^(2) -15x=54-24x+9x-4x^(2) \\2x^(2) -15x=54-15x-4x^(2) \\`

By adding both sides by
`15x`

`2x^(2) =54-4x^(2) \\`

Adding both sides by
`4x^(2)`

`6x^(2) =54`

Dividing both sides by 6

`x^(2) =9`

Taking root both sides

`\sqrt[2]{x^(2) } =\sqrt[2]{9} \\x=\sqrt[2]{3*3} \\x=3`

Thus, the number is 3.