The Nováks baked wedding cakes. They took a quarter of them to their relatives in Moravia, gave a sixth to their colleagues at work, and gave a ninth to their neighbors. If they had three more cakes left, it would be half of the original number. How many cakes did they bake?
The Nováks were given a quarter, a sixth, and a ninth of the cakes, which is 3 more than half of all:

$$
\frac{1}{4}+\frac{1}{6}+\frac{1}{9}=\frac{19}{36}
$$

Half is $\frac{18}{36}$. They distributed $\frac{1}{36}$ more. $\frac{1}{36}$ represents 3 cakes, so the total number of cakes was $36 \cdot 3=108$. They baked 108 cakes.

[Adding fractions ... 2 points, 1/36 are 3 cakes ... 2 points, correct answer ... 2 points.]