Question

the denominator of a rational number is greater than its numerator by 14.if the numerator and denominator are both increased by 5 the new number obtained is 11/18 find the original rational number

Answer 1

Step-by-step explanation:

Lets take the numerator as x then denominator will become (x+14) .

If the numerator and denominator is increased by 5 then the new number is 11/18 the original rational number. New number is (x+5)/(x+19).

$\frac{(x + 5)}{(x + 19)} = \frac{11}{18} \frac{x}{(x + 14)} = >$

$18(x + 14)(x + 5)= 11x(x + 19)= >$

$18( {x}^{2} + 14x + 5x + 70) = 11 {x}^{2} +$

$209x = > 18 {x}^{2} + 342x + 1260 =$

$11 {x}^{2} + 209x = > 18 {x}^{2} - 11 {x}^{2} +$

$342x - 209x + 1260 = 0 = > 7{x}^{2} +$

$133x + 1260 = 0 = > {x}^{2} + 19x +$

$180 = 0$

Determinant is negative so no value of x can satisfy the above conditions so it is not possible. Hope it helps you.