Problem 1. During the school year, Kosta took several math tests and scored a certain number of points. If Kosta scores 89 points on the next math test, then the average number of points earned from the tests will be 91. However, if on the next test he scores 64, then the average number of points will be 86. How many math tests has Kosta taken so far?
Solution. Let $n$ be the number of math tests taken so far, and $x$ be the total number of points earned from these tests. If on the next math test Costa scores 89 points, then the total number of points earned will be $x+89$, and the number of tests will be $n+1$. According to this, we get the equation $\frac{x+89}{n+1}=91$. If on the next math test Costa scores 64 points, then the total number of points earned will be $x+64$, and the number of tests remains the same, i.e., $n+1$. Then we get the equation $\frac{x+64}{n+1}=86$. If we divide these equations, we get $\frac{x+89}{x+64}=\frac{91}{86}$, from which we find $x=366$. Finally, $n+1=\frac{366+89}{91}$, i.e., $n=4$. Therefore, Costa has taken 4 math tests.