Question

The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted from both its numerator and denominator, the new fractionequals 2 over 3 . What is the original fraction?

Answer 1

`(25)/(34)`

Step-by-step explanation:

Here, we want to get the original fraction

Let us have the original fraction as follows:

`(x)/(y)`

From the question, the denominator is greater than the numerator by 9

Mathematically, we have that as:

`y-x\text{ = 9}`

We proceed with the second sentence as follows:

`\begin{gathered} (x-7)/(y-7)\text{ = }(2)/(3) \\ 3(x-7)\text{ = 2(y-7)} \end{gathered}`

From the first equation, we have it that:

`y\text{ = x + 9}`

Substitute this into the second equation as follows:

`\begin{gathered} 3(x-7)\text{ = 2(x+9-7)} \\ 3x-21\text{ = 2x+18-14} \\ 3x-21\text{ = 2x + 4} \\ 3x-2x\text{ = 4+21} \\ x\text{ = 25} \end{gathered}`

From above, we recall that:

`\begin{gathered} y\text{ = x + 9} \\ y\text{ = 9 + 25} \\ y\text{ = 34} \end{gathered}`

The original fraction is thus:

`(25)/(34)`