The Fraction

The denominator of a Fraction is greater than the numerator by 4. if 11 is added to the numerator and one subtracted from the denominator, the value of the fraction obtained is 7/3. What is the original fraction?

Correct answer:

x =  3/7

Step-by-step explanation:

$$\begin{gathered} d=4+n \\ (11+n)=7/3\cdot (d-1) \\ d-n=4 \\ 7d-3n=40 \\ Pivot:Row1\leftrightarrow Row2 \\ 7d-3n=40 \\ d-n=4 \\ Row2-\frac{1}{7}\cdot Row1\to Row2 \\ 7d-3n=40 \\ -0.57n=-1.71 \\ n=\frac{-1.71428571}{-0.57142857}=3 \\ d=\frac{40+3n}{7}=\frac{40+3\cdot 3}{7}=7 \\ d=7 \\ n=3 \\ x=\frac{n}{d}=\frac{3}{7}=0.4286 \end{gathered}$$

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