Question

15. The numerator of a rational number is 5 less than its
denominator. If 2 is subtracted from the numerator and 2
is added to the denominator, the number becomes 2/5.
Find the rational number.​

Answer 1

Answer:

According to the question,

let the denominator be x

so numerator is x-5

if 2 is subtracted from the numerator which is x-5-2= x-7

and 2 is added to the denominator which is x+2.

now framing the equation

x-7/x+2 = 2/5

by cross multiplication

5(x-7) = 2(x+2)

5x-35 = 2x+4

bring all the variables to one side and constants to one side,

5x-2x = 4+35

3x = 39

x = 39/3 = 13

hence the rational number is

x-5/13= 13-5/13= 8/13

Step-by-step explanation: