1. On the meadow, there are children and adults. The percentage of boys among all children is equal to the percentage of girls among all present people and also the number of all adults. How many boys, girls, and adults are on the meadow?
SOLUTION. Let's denote $c, d$ and $v$ as the number of boys, girls, and adults on the meadow, respectively. We have

$$
\frac{100 c}{c+d}=\frac{100 d}{c+d+v}=v
$$

From the first equality, we get $d^{2}=c^{2}+v c$, which we substitute into the equality between the first and third expression, which we first rearrange to the form $v d=(100-v) c$ and then square. After rearrangement, we get

$$
v^{3}=200 c(50-v)
$$

From this, it follows that $v$ is divisible by 10 and $v<50$. By testing all four possibilities $(v=10, v=20, v=30, v=40)$, we find that we get an integer $c$ only for $v=40$. Then $c=32, d=48$.

There are 32 boys, 48 girls, and 40 adults on the meadow.

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