Question

A number is subtracted from $\frac{2}{5}$ and the difference is multiplied by $10$, the result is $-16$, find the number.

Answer 1

Step 1: Identifying given data and simplifying.

Let the number be $\mathrm{x}$

Subtracting the number from $\frac{2}{5}$ will give you $\left(\frac{2}{5}-\mathrm{x}\right)$

And multiplying the difference by $10$will result into $10\left(\frac{2}{5}-\mathrm{x}\right)$

According to given condition,

$10\left(\frac{2}{5}-\mathrm{x}\right)=-16$

Step 2: Finding the value of $\mathrm{x}$

We have, $10\left(\frac{2}{5}-\mathrm{x}\right)=-16$

$$\begin{gathered} \Rightarrow \frac{10\times 2}{5}-10\times \mathrm{x}=-16 \\ \Rightarrow \frac{20}{5}-10\mathrm{x}=-16 \\ \Rightarrow \frac{{\displaystyle \stackrel{4}{\cancel{20}}}}{\cancel{5}}-10\mathrm{x}=-16 \\ \Rightarrow 4-10\mathrm{x}=-16 \\ \Rightarrow -10\mathrm{x}=-16-4 \\ \Rightarrow -10\mathrm{x}=-20 \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{2}{\cancel{-20}}}}{\cancel{-10}} \\ \Rightarrow \mathrm{x}=2 \end{gathered}$$

Hence the number is $2$.