Question

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1.

What is the numerator of the fraction?

Answer 1

Hey there!

n=numerator and d=denominator
(n+3)/d=3/4
n/(d+7)=1
n=d+7
(d+7+3)/d=3/4 substitute d+7 for n.
(d+10)/d=3/4

) 4(d+10)=3d multiply each side by 4d
4d+40=3d=-40
n=-40+7
n=-33

Answer 2

Answer: The numerator of the given fraction is 9.

Step-by-step explanation: Given that if the numerator of a fraction is increased by 3, the fraction becomes
`(3)/(4)` and if the denominator is decreased by 7, the fraction becomes 1.

We are to find the numerator of the function.

Let x and y represents the numerator and denominator of the given function.

Then, according to the given information, we have

`(x+3)/(y)=(3)/(4)\\\\\Rightarrow 4(x+3)=3y\\\\\Rightarrow 4x+12=3y\\\\\\\Rightarrow y=(4x+12)/(3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and

`(x)/(y-7)=1\\\\\Rightarrow x=y-7\\\\\Rightarrow y=x+7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Equating the values of y from equations (i) and (ii), we get

`(4x+12)/(3)=x+7\\\\\Rightarrow 4x+12=3(x+7)\\\\\Rightarrow 4x+12=3x+21\\\\\Rightarrow 4x-3x=21-12\\\\\Rightarrow x=9.`

Thus, the numerator of the given fraction is 9.