Adjust numerators

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8. If the numerator and the denominator of the same fraction are each increased by 1, the fraction becomes 1/2. Find the fraction.

Final Answer:

x =  3/7

Step-by-step explanation:

$$\begin{gathered} x=\frac{a}{b} \\ \frac{a+2}{b+1}=\frac{5}{8} \\ \frac{a+1}{b+1}=\frac{1}{2} \\ (a+2)\cdot 8=5\cdot (b+1) \\ (a+1)\cdot 2=1\cdot (b+1) \\ 8a-5b=-11 \\ 2a-b=-1 \\ Row2-\frac{2}{8}\cdot Row1\to Row2 \\ 0.25b=1.75 \\ b=\frac{1.75}{0.25}=7 \\ a=\frac{-11+5b}{8}=\frac{-11+5\cdot 7}{8}=3 \\ a=3 \\ b=7 \\ x=\frac{a}{b}=\frac{3}{7}=0.4286 \end{gathered}$$

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