Question

Yaneev thinks of a number $y$. He subtracts three from the number, then doubles it. Then he subtracts three again and doubles the number again. The result is his original number $y$. What is $y$?

Answer 1

Find the original number $\mathit{y}$.

Given that number $y$ should be subtracted with $3$ and to double the number.

This gives the number $2\left(y-3\right)$.

Now, subtract $3$ again and double the number.

This gives the resultant number $2\left(2\left(y-3\right)-3\right)$.

Now, the resultant number is equal to the original number $y$:

$$\begin{gathered} 2\left(2\left(y-3\right)-3\right)=y \\ \Rightarrow 2\left(2y-6-3\right)=y \\ \Rightarrow 2\left(2y-9\right)=y \\ \Rightarrow 4y-18=y \\ \Rightarrow 4y-y=18 \\ \Rightarrow 3y=18 \\ \Rightarrow y=\frac{18}{3} \\ \Rightarrow y=6 \end{gathered}$$

Hence, the value of the original number $\mathit{y}$ is $\mathbf{6}$.