Question

the numerator of a rational number is 8 greater than its denominator. if the numerator becomes twice and the denominator is increased by 3, the new number becomes 3. find the original number and check your answer​

Answer 1

Let the denominator of the rational number be x.

So as per the given condition, the numerator will be x+ 8

The rational number will be $\frac{x + 8}{8}$

Now, According to the Question the rational no. will be

$2\frac{x + 8}{x + 3} = \frac{3}{1}$

By Cross Multiplying

2(x + 8) = 3(x + 3)

=> 2x + 16 = 3x + 9

=> 2x - 3x = 9 - 16

=> -x = -7

=> x = 7.

Now, Putting x = 7 in rational number

So, the Original Number is 15/8.

Answer 2

Step-by-step explanation:

• let the original number be x+8/x

if the denominator is multiplied by 2 and denominator is increased by 3 then the new number is 3

• 2(x+8)/x+3=3

then 2x+16=3x+9

then x=7

there fore by substituting the values in the original number the answer is 15/7