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

Answer:

3

Step-by-step 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 $\div$ 6 more than the number = 4 less than 9 times the reciprocal of the number

Then the equation will be:-

$\frac{2x-15}{6+x} =9\times\frac{1}{x} -4\\\\ \frac{2x-15}{6+x} =\frac{9}{x} -4\\\\ \frac{2x-15}{6+x} =\frac{9-4x}{x}$

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

$\sqrt[2]{x^{2} } =\sqrt[2]{9} \\x=\sqrt[2]{3\times3} \\x=3$

Thus, the number is 3.