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the question is the following one: a student attended to a certain number of exams, his grade's average is 25 ( the possible grades are 18-30), in the next exam he gets 30 and his average raises to 26, how many exams he took? the correct answer is 5, but how am i supposed to get it? i tried doing things with the average definition using the summation but i didn't come out with any solution, anyone knows how to solve this?

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$$\cfrac{25n+30}{n+1}=26$$ $25n$ is the sum of the grades in the $n$ exams. Multiply both sides by $n+1$ $$25n+30=26(n+1)=26n+26$$ $$25n+30=26n+26$$ $$n=4$$ Where $n$ is how many exams he took before the one he scored 30, so taking that one into account , we have a total of $4+1=5$ exams.

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That one exam score was $5$ points above the average but raised the average by just $1$ point. That means it accounts for just $1/5$ of the exams. So it was the fifth exam.

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