Question

Amina thinks of a number and subtracts $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ from it. She multiplies the result by $8$. The result now obtained is $3$ times the same number she thought of. What is the number?

Answer 1

Let the number be $x$,

According to the question:

$\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ subtracted from the number $x$, we get, $(x-\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.)$

now, multiplies the result by $8$, we get $3$ times the same number in equal, so, we have,

$(x-\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.)\times 8=3x$

Solving for x we get:

$8x-\raisebox{1ex}{$40$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=3x$

Rearranging the like terms and solving we get:

$$\begin{gathered} 8x-3x=\raisebox{1ex}{$40$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ 5x=20 \\ x=4 \end{gathered}$$

Hence, the number is $4$.