The sum of numerator and denominator is equal to 7 . Four times the numerator is 8 less than 5 times the denominator. Find the fraction.

Asked by archana | 30th Jan, 2017, 09:09: PM

Expert Answer:

begin mathsize 16px style Let space the space fraction space be space straight x over straight y.
According space to space the space first space condition comma
straight x plus straight y space equals space 7 space.... left parenthesis 1 right parenthesis
According space to space the space second space condition comma
4 straight x equals 5 straight y minus 8
rightwards double arrow 4 straight x minus 5 straight y equals negative 8 space... left parenthesis 2 right parenthesis
Multiplying space left parenthesis 1 right parenthesis space by 5 comma space we space get space
5 straight x plus 5 straight y space equals 35 space..... left parenthesis 3 right parenthesis
Adding space left parenthesis 2 right parenthesis space and space left parenthesis space 3 right parenthesis comma space we space get
9 straight x space equals space 27
rightwards double arrow straight x equals 3
Substituting space in space left parenthesis 1 right parenthesis comma space we space get
3 plus straight y space equals space 7 rightwards double arrow straight y equals 4
So comma space the space fraction space is space 3 over 4. end style

Answered by Rebecca Fernandes | 31st Jan, 2017, 08:58: AM