Question

A number is such that when you multifly it by 5/2 and add 2/3 to the product you get -7/12, what is the number?

Answer 1

AnswEr :

-1/2

$\bf{\large{\underline{\underline{\rm{Given\::}}}}}$

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

$\bf{\large{\underline{\underline{\rm{To\:find\::}}}}}$

The number.

$\bf{\large{\underline{\underline{\tt{\red{Explanation\::}}}}}}$

Let the number be r

A/q

$\dashrightarrow\tt{\dfrac{5}{2} \times r +\dfrac{2}{3} =\dfrac{-7}{12} }\\\\\\\\\dashrightarrow\tt{\dfrac{5r}{2} =\dfrac{-7}{12} -\dfrac{2}{3} }\\\\\\\\\dashrightarrow\tt{\dfrac{5r}{2} =\dfrac{-7-8}{12} }\\\\\\\\\dashrightarrow\tt{\dfrac{5r}{2} =\dfrac{-15}{12} }\\\\\\\\\dashrightarrow\tt{60r\:=\:-30}\\\\\\\\\dashrightarrow\tt{r\:=\:\cancel{\dfrac{-30}{60} }}\\\\\\\\\dashrightarrow\tt{\red{r\:=\:-\dfrac{1}{2} }}$

∴ The number is $\bf{-\dfrac{1}{2} }$.

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

___________________________

➠ To Find :

We have to find the number.

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➠ Solution :

Let the number be x.

So, A. T. Q

$\sf{\implies \frac{5}{2}(x) + \frac{2}{3} = \frac{-7}{12}} \\ \\ \sf{\implies \frac{5x}{2} = \frac{-7}{12} - \frac{2}{3}} \\ \\ \bf{Taking \: LCM} \\ \\ \sf{\implies \frac{5x}{2} = \frac{-7 - 8}{12}} \\ \\ \sf{\implies \frac{5x}{2} = \frac{-15}{12}} \\ \\ \sf{\implies 5x = \frac{-15}{\cancel{12}} \times \cancel{2}} \\ \\ \sf{\implies x = \frac{-\cancel{15}}{6} \times \frac{1}{\cancel{5}}} \\ \\ \sf{\implies x = \frac{-\cancel{3}}{\cancel{6}}} \\ \\ \sf{\implies x = \frac{-1}{2}} \\ \\ \sf{\therefore Number = \frac{-1}{2}}$