Question

A rational number is such that when you multiply it by 5/2 and add 2/3 to the product , to get -7/12. What is the number?​

Answer 1

Step-by-step explanation:

$Given \begin{cases}A\: rational \:number\:if \:multiply\: by\: {\dfrac {5}{2}}\:and\:add\:with\:{\dfrac {2}{3}}\:gives\:{\dfrac {-7}{12}}\end {cases}$

To find:-

The number

Solution:-

Let the rational number=${\dfrac{x}{y}}$

• According to question

$({\dfrac {x}{y}}×{\dfrac {5}{2}})+{\dfrac {2}{3}}={\dfrac {-7}{12}}$

${:}\mapsto$${\dfrac {5x}{2y}}+{\dfrac {2}{3}}={\dfrac {-7}{12}}$

${:}\mapsto$${\dfrac {15x+4y }{6y}}={\dfrac {-7}{12}}$

${:}\mapsto$$-42y=12 (15x+4y)$

${:}\mapsto$$-42y=180x+48y$

${:}\mapsto$$180x=-48y-42y$

${:}\mapsto$$180x=-90y$

${:}\mapsto$$y={\dfrac {180x}{-90}}$

${:}\mapsto$$y=-2x$

_____________________________

Now

• The number =

${\dfrac {x}{y}}$

${:}\mapsto$${\dfrac {{\cancel {x}}}{-2{\bcancel {x}}}}$

${:}\mapsto$${\underline{\boxed{\bf{{\dfrac {1}{(-2)}}}}}}$

${\therefore}$The number=${\dfrac {1}{(-2)}}$

Verification:-

$({\dfrac {1}{(-2)}}×{\dfrac {5}{2}})+{\dfrac {2}{3}}={\dfrac{-7}{12}}$

${:}\mapsto$${\dfrac {5}{-4}}+{\dfrac {2}{3}}={\dfrac {-7}{12}}$

${:}\mapsto$${\dfrac{15+(-8)}{12}}={\dfrac {-7}{12}}$

${:}\mapsto$${\dfrac {15-8}{12}}={\dfrac{7}{12}}$

${:}\mapsto$${\dfrac {-7}{12}}={\dfrac {-7}{12}}$

LHS = RHS

Hence verified