2. Before the lesson, Nestor Petrovich wrote several words on the board. When the bell rang for the lesson, he noticed a mistake in the first word. If he corrects the mistake in it, the words with mistakes will make up $24 \%$, and if he erases the first word from the board altogether, the words with mistakes will make up $25 \%$. What percentage of the total number of words written did the words with mistakes constitute before the lesson started?
Answer: $28 \%$.

## Solution:

Let there be $n$ words written on the board before the lesson, of which $x$ have errors. If the error in the first word is corrected, then there will be $x-1$ words with errors out of $n$, and by the condition $x-1=0.24 n$. If a word with an error is erased, then there will be $x-1$ words with errors out of $n-1$, and by the condition $x-1=0.25(n-1)$. Then $0.24 n=0.25(n-1)$, from which $0.01 n=0.25$.

Thus, $n=25$, and $x=0.24 n+1=0.24 \cdot 25+1=7$.

Therefore, before the lesson, words with errors made up $7 / 25$ of the total number of words, which is $28 \%$.

## Criteria:

A correct answer without a correct justification and without an example of how many words and words with errors it was obtained for, -1 point.

A correct answer without a correct justification, but with an example of how many words and words with errors it was obtained for, - 2 points.

Finding a suitable example of words without justification of why there cannot be another option (and if this justification does not follow from the solution), does not add points to the correct answer.