## Task 2 - 150522

For the following five equations, natural numbers are to be substituted for the letters $x, y, z, u, v$ so that true statements result. The same letters represent the same numbers.

$$
\begin{aligned}
& x=y: 40 \\
& z=4 \cdot u \\
& u=280: 7 \\
& 160=v+40 \\
& y=z+v
\end{aligned}
$$
From equation (3), a true statement arises only when $u=40$ is substituted, because $280: 7=40$. Subsequently, a true statement arises from (2) only when $z=160$ is substituted, because $4 \cdot 40=160$. Equation (4) becomes true only when $v=120$ is substituted; because $160=120+40$, while the sum of 40 and any number other than 120 results in a number other than 160.

Because $160+120=280$, equation (5) becomes true only for $y=280$, and because $280: 40=7$, equation (1) becomes true only for $x=7$.