Martin decided to spend all his savings on sweets. He found out that he could buy three lollipops and $3 \mathrm{dl}$ of cola or $18 \mathrm{dkg}$ of yogurt-covered raisins or $12 \mathrm{dkg}$ of yogurt-covered raisins and half a liter of cola. In the end, he bought one lollipop and 6 dl of cola. How many grams of yogurt-covered raisins did he still have left?

(Bednářová)
Let's denote:

| 1 windmill | $\ldots v$ |
| :--- | :--- |
| 1 deciliter of cola | $\ldots k$ |
| 1 dekagram of raisins | $\ldots r$ |
| the unknown amount of raisins (in dekagrams) | $\ldots x$ |

Since Martin wanted to spend all his savings each time, we can symbolically represent the individual relationships using simple equations as follows:

$$
\begin{gathered}
3 v+3 k=18 r, \\
12 r+5 k=v+6 k+x r
\end{gathered}
$$

(2 points for setting up the system of equations)

The first relationship means that 3 windmills and 3 deciliters of cola have the same value as 18 dekagrams of raisins. Here, we can divide both sides of the equation by 3, i.e., we get:

$$
v+k=6 r \text {. }
$$

The second relationship means that 12 dekagrams of raisins and 5 deciliters of cola (i.e., half a liter) have the same value as 1 windmill, 6 deciliters of cola, and an unknown amount of raisins $x$. Here, we can modify the equation by subtracting $5 k$ from both sides, i.e.,

$$
12 r=v+k+x r \text {. }
$$

If we write both modified equations one below the other, we get:

$$
\begin{gathered}
v+k=6 r \\
12 r=v+k+x r .
\end{gathered}
$$

Now, substituting the first equation into the second, we get the equation:

$$
12 r=6 r+x r \text {. }
$$

To achieve equality, $x$ must be 6 dekagrams of raisins, which is 60 grams.

Therefore, Martin had enough money left to buy 60 grams of raisins in yogurt.

(Full solution 6 points)