## Task B-1.2.

At the graduation dance, there were a total of 46 girls and boys. The first girl danced with 9 boys, and each subsequent girl danced with one more boy. If the last girl danced with all the boys present, how many girls and how many boys were at the graduation dance?
## Solution.

Let $n$ be the number of girls present at the graduation dance. Then the number of boys is $46-n$.

The first girl danced with 9 boys, the second with 10 boys or $9+1$, the third with 11 or $9+2$, ..., the last, i.e., the $n$-th girl with $9+(n-1)=n+8$ boys.

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This number is equal to the total number of boys, so we have $46-n=n+8$ boys.

From this equation, it follows that $n=19$.

Therefore, there were 19 girls and 27 boys at the dance.
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