A fraction becomes 9/11, if 3 is added to both the numerator and denominator. If 3 is added to both the numerator and denominator it becomes 5/6 as well. So what will be the original fraction?

1 Answer
Jan 27, 2018

The original fraction is 27/332733

Explanation:

Let's translate in math expressions:

1) x/y=9/11xy=911

2) (x+3)/(y+3)=5/6x+3y+3=56

The expression 1) is equivalent to x=9/11yx=911y

then we will substitute in expression 2) and get:

(9/11y+3)/(y+3)=5/6911y+3y+3=56

that is equivalent to the following:

(9/11y+3)*6=5(y+3)(911y+3)6=5(y+3)

Let's expand and get

54/11y+18=5y+155411y+18=5y+15

The let's solve the equation and get y:

54/11y-5y=15-185411y5y=1518

(54-55)/11y=-3545511y=3

-1/11y=-3111y=3

y=33y=33

then we will find x

x=9/11y=9*33/11=27x=911y=93311=27

The fraction is 27/332733