Question

The numerator of a fraction is 6 times its denominator. If the numerator is increased by 5 and the denominator is decreased by 1, the fraction becomes 3/2. Find the fraction. Please help me to solve only in 1 variable.

Answer 1

Answer:

This the solution for given question.

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Answer 2

Answer:

$\boxed{\bf 6}$

Step-by-step explanation:

$let \ the \ denominator \ be \ x\\\text{The numerator of a fraction is 6 times its denominator.} \\ \text{numerator of the fraction = 6x } \\\\ \text{If the numerator is increased by 5 and the denominator is decreased by 1, }\\ \text{the fraction becomes 3/2.} \\\\ \frac{6x+5}{x-1} =\frac{3}{2} \\\\2(6x+5)=3(x-1) \\\\12x+30=3x-3\\\\12x-3x=-3-30\\\\ 9x=-33 \\\\3x=-11\\\\x=\frac{-11}{3} \\\\ \rightarrow denominator=\frac{-11}{3} \\\\ \rightarrow numerator=6(\frac{-11}{3} )$

$=>fraction=\frac{numerator}{denominator} \\\\ =>fraction = \frac{6(\frac{-11}{3} )}{(\frac{-11}{3})} =\frac{6}{1}$

hope it helps..!