Question

The numerator of a fraction is 1 less than the denominator. If 3 is added to each of the

numerator and demoninator, the fraction is increased by

3
/28

. Find the fraction.

Answer 1

Let the Numerator of the fraction be x
and Denominator be y

x = y - 1

x+3/y+3 = x/y + 3/28
x+3/y+3 = 28x+3y/28y

y-1+3/y+3 = y+2/y+3
28x+3y/28y = 28(y-1)+3y/28y
= 28y-28+3y/28y
= 31y-28/28y

y+2/y+3 = 31y-28/28y
28y (y+2) = (31y-28)(y+3)
28y2 + 56y = 31y2 + 93y - 28y - 84

3y2 + 9y - 84 = 0
3y2 + 21y - 12y -84 = 0
3y(y+7) -12(y+7) = 0
(3y-12) (y+7) = 0

As y cannot be negative ..
3y - 12 = 0
3y = 12
y = 4

x = y - 1
x = 4 - 1
x = 3

Fraction = x/y = 3/4

Hope this helps!!
cheers! (:

★‡★

Answer 2

Answer:

Step-by-step explanation:

Let the Numerator of the fraction be x

and Denominator be y

x = y - 1

x+3/y+3 = x/y + 3/28

x+3/y+3 = 28x+3y/28y

y-1+3/y+3 = y+2/y+3

28x+3y/28y = 28(y-1)+3y/28y

= 28y-28+3y/28y

= 31y-28/28y

y+2/y+3 = 31y-28/28y

28y (y+2) = (31y-28)(y+3)

28y2 + 56y = 31y2 + 93y - 28y - 84

3y2 + 9y - 84 = 0

3y2 + 21y - 12y -84 = 0

3y(y+7) -12(y+7) = 0

(3y-12) (y+7) = 0

As y cannot be negative ..

3y - 12 = 0

3y = 12

y = 4

x = y - 1

x = 4 - 1

x = 3

Fraction = x/y = 3/4