Question

the sum of numerator and denominator of a fraction is 12 if 1 is added to both the numerator and denominator of the fraction becomes 3 by4 find the fraction

Answer 1

x = numerator

y = denominator

The sum of x and y is 12:

x+y=12

and

xy+3=12

from the second:

x=12(y+3)

into the first:

12(y+3)+y=12

y+3+2y=24

3y=21

y = 21/3

y=7

and so:

x=12−7=5

.'. numerator = 5

& Denominator=7

Fraction = 5/7

Answer 2

sum of numerator and denominator is =12
x+y=12 ----) 1)
if 1 is added fraction is = 3/4
x+1/y+1=3/4
4(x+1)=3(y+1)
4x+4=3y+3
x= 3y-1/4---) 2)
substitute 2) in 1)
3y-1/4+y=12
7y-1/4=12
7y-1=48
7y=49
y=7-----) 3)
substitute 3) in 1)
x+7=12
x=5
therefore fraction is 5/7