Explanations:
Let the numerator of the fraction be x and let the denominator be y.
Hence, the original fraction is:
[tex]\frac{x}{y}[/tex]It is given that the denominator is 3 more than the numerator. It follows that:
[tex]y=x+3[/tex]It is also given that when both the numerator and denominator are increased by 4, the new fraction is equal to 3/4. This implies mathematically to the equation:
[tex]\frac{x+4}{y+4}=\frac{3}{4}[/tex]Simplify this equation:
[tex]\begin{gathered} 4(x+4)=3(y+4) \\ \Rightarrow4x+16=3y+12 \end{gathered}[/tex]Substitute y=x+3 into this equation:
[tex]4x+16=3(x+3)+12[/tex]Solve the equation for x:
[tex]\begin{gathered} \Rightarrow4x+16=3x+9+12 \\ Collect\text{ like terms:} \\ \Rightarrow4x-3x=9+12-16 \\ \Rightarrow x=5 \end{gathered}[/tex]Substitute x=5 into the equation y=x+3:
[tex]y=5+3=8[/tex]Hence, x=5, and y=8.
It follows that the original fraction is 5/8.
Answer:
The original fraction is 5/8.
