Question

(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x

Answer 1

let's firstly convert the mixed fractions to improper fractions and them proceed.

`\stackrel{mixed}{6(1)/(7)}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3(5)/(9)}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4(1)/(6)}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1(1)/(3)}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill`

`\cfrac{ ~~ (6(1)/(7))/(x)+3(5)/(9) ~~ }{4(1)/(6)}~~ = ~~1(1)/(3)\implies \cfrac{ ~~ ( ~~ (43)/(7) ~~ )/(x)+(32)/(9) ~~ }{(25)/(6)}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ (43)/(7x)+(32)/(9) ~~ }{(25)/(6)}~~ = ~~\cfrac{4}{3}`

`\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3(1)/(14)=x`