## Task 7 - V00607 = V00503

To an imagined number, 16 is added, then multiplied by 7, followed by subtracting 8, and finally dividing by 9. The result is 22 remainder 4.

What is the imagined number?
Let $x$ be the thought number. Then the operations yield the term

$$
((x+16) \cdot 7-8): 9
$$

This term should result in 22 with a remainder of 4, i.e.,

$$
((x+16) \cdot 7-8)=9 \cdot 22+4
$$

Step-by-step simplification and rearrangement yields

$$
\begin{aligned}
((x+16) \cdot 7-8) & =9 \cdot 22+4 \\
(x+16) \cdot 7-8 & =198+4 \\
(x+16) \cdot 7 & =202+8 \\
x+16 & =210: 7 \\
x & =30-16=14
\end{aligned}
$$

The thought number is 14.