4. Throughout the year, Marko took several exams and scored a certain number of points on them. If Marko were to score 89 points on his next exam, his average score on the exams would be 91. However, if he were to score 64 points on the next exam, his average score on the exams would then be 86. How many exams has Marko taken so far?
First method:

Let $n$ be the number of exams Marko has written so far, and $x$ the sum of the scores achieved on them.

From the conditions of the problem, it is clear that:

$\frac{x+89}{n+1}=91, \frac{x+64}{n+1}=86$

$1 \text{ POINT}$

From both equations, express $x$:

$x=91 \cdot(n+1)-89 \quad$ and $\quad x=86 \cdot(n+1)-64$

$1 \text{ POINT}$

Equate the right-hand sides:

$91 \cdot(n+1)-89=86 \cdot(n+1)-64$

$1 \text{ POINT}$

$91 n+91-89=86 n+86-64$

$91 n+2=86 n+22$

$91 n-86 n=22-2$

| $5 n=20$ | 1 POINT |
| :--- | ---: |
| $n=4$ | 1 POINT |
| Marko has written 4 exams so far. | 1 POINT |
| ......................................................................................................... 6 POINTS. |  |