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?

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Answer 1 · 2018-01-27T07:35:49

The original fraction is #27/33#

Let's translate in math expressions:

1) #x/y=9/11#

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

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

then we will substitute in expression 2) and get:

#(9/11y+3)/(y+3)=5/6#

that is equivalent to the following:

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

Let's expand and get

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

The let's solve the equation and get y:

#54/11y-5y=15-18#

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

#-1/11y=-3#

#y=33#

then we will find x

#x=9/11y=9*33/11=27#

The fraction is #27/33#