Solution:
Let the denominator be represented by a
The numerator of a certain fraction is four times the denominator
Then, the numerator will be 4a
The original fraction is
[tex]\frac{4a}{a}[/tex]If 10 is added to both the numerator and the denominator, as shown below
[tex]\frac{4a+10}{a+10}[/tex]The resulting fraction is equivalent to 2, i.e.
[tex]\frac{4a+10}{a+10}=2[/tex]Solve for a
Crossmultiply
[tex]\begin{gathered} 4a+10=2(a+10) \\ Open\text{ the brackets on the right side of the equation} \\ 4a+10=2a+20 \\ Collect\text{ like terms} \\ 4a-2a=20-10 \\ 2a=10 \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}=\frac{10}{2} \\ a=5 \end{gathered}[/tex]Where a = 5,
The original fraction is
[tex]\frac{4a}{a}=\frac{4(5)}{5}=\frac{20}{5}[/tex]Hence, the original fraction is
[tex]\frac{20}{5}[/tex]