Question

17) If you subtract 1/2 from a number and multiply the result by 1/2 , you get 1/6 what is the number?​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow let\:the\:number\:be\:x$

$\sf\dashrightarrow \text{ if you subtract } \dfrac{1}{2}\: \:from a\:number(x)\: and\:multiply\:the\:result\:by\:\dfrac{1}{2}$ $\sf we\:get\:\dfrac{1}{6}$

$\sf\therefore \bigg( x - \dfrac{1}{2} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:NUMBER.$

$\large\underline\bold{SOLUTION,}$

$\sf\dashrightarrow \bigg( x - \dfrac{1}{2} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\sf\implies \bigg( \dfrac{2x-1}{2} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\sf\implies 2x-1= \dfrac{1}{6} \times 4$

$\sf\implies 2x-1= \dfrac{1}{\cancel{6}} \times \cancel{4}$

$\sf\implies 2x-1=\dfrac{2}{3}$

$\sf\implies 2x= \dfrac{2}{3 } +1$

$\sf\implies 2x= \dfrac{2+3}{3 }$

$\sf\implies 2x= \dfrac{5}{3 }$

$\sf\implies x= \dfrac{5}{3} \times \dfrac{1}{2}$

$\sf\implies x= \dfrac{5}{6}$

$\large{\boxed{\bf{ \star\:\: x= \dfrac{5}{6}\:\: \star}}}$

$\large\underline\bold{THE\:NUMBER\:IS\:\:\dfrac{5}{6} .}$

✯VERIFICATION,

$\sf\therefore \bigg( x - \dfrac{1}{2} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\sf\implies \bigg( \dfrac{5}{6} - \dfrac{1}{2} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\sf\implies \bigg( \dfrac{10-6}{12} \bigg) \times \dfrac{1}{2} = \dfrac{1}{6}$

$\sf\implies \dfrac{4}{12} \times \dfrac{1}{2}= \dfrac{1}{6}$

$\sf\implies \dfrac{\cancel{4}}{12} \times \dfrac{1}{\cancel{2}}= \dfrac{1}{6}$

$\sf\implies \dfrac{2}{12}= \dfrac{1}{6}$

$\sf\implies \cancel \dfrac{2}{12}= \dfrac{1}{6}$

$\sf\implies \dfrac{1}{6}= \dfrac{1}{6}$

$\sf\therefore L.H.S= R.H.S$

HENCE PROVED✔

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