Numerator and denominator

If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35.
What is the original fraction?

Final Answer:

x =  3/14

Step-by-step explanation:

$$\begin{gathered} x=\frac{a}{b} \\ {r}_1=100\%+200\%=1+\frac{200}{100}=3 \\ {r}_2=100\%+150\%=1+\frac{150}{100}=2.5 \\ \frac{a\cdot r_1}{b\cdot r_2}=\frac{9}{35} \\ \frac{a}{b}\cdot \frac{r_1}{r_2}=\frac{9}{35} \\ x\cdot \frac{r_1}{r_2}=\frac{9}{35} \\ x\cdot r=\frac{9}{35} \\ r=\frac{r_1}{r_2}=\frac{3}{\frac{5}{2}}=\frac{6}{5}=1\frac{1}{5}=1.2 \\ x=\frac{9}{35}/r=\frac{9}{35}/\frac{6}{5}=\frac{9}{35}:\frac{6}{5}=\frac{9}{35}\cdot \frac{5}{6}=\frac{9\cdot 5}{35\cdot 6}=\frac{45}{210}=\frac{3}{14}=0.2143 \end{gathered}$$

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