Numerators and denominators 2

A fraction becomes 2 when 1 is added to both the numerator and denominator and it becomes 3 when 1 is subtracted from both numerator and denominator. Find the difference of numerator and denominator.

Final Answer:

d =  4

Step-by-step explanation:

$$\begin{gathered} w=\frac{a}{b} \\ \frac{a+1}{b+1}=2 \\ \frac{a-1}{b-1}=3 \\ (a+1)=2(b+1) \\ (a-1)=3(b-1) \\ (a+1)=2\cdot (b+1) \\ (a-1)=3\cdot (b-1) \\ a-2b=1 \\ a-3b=-2 \\ Row2-Row1\to Row2 \\ -b=-3 \\ b=\frac{-3}{-1}=3 \\ a=1+2b=1+2\cdot 3=7 \\ a=7 \\ b=3 \\ w=\frac{a}{b}=\frac{7}{3}=2\frac{1}{3}\doteq 2.3333 \\ d=a-b=7-3=4 \end{gathered}$$

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