1. If from one page of a book three letters are removed from each line and then two such lines are removed, the number of all letters will decrease by 145. If, on the other hand, we add four letters to each line and write three such lines, then the number
of all letters will increase by 224. How many lines are there on that page and how many letters are there in each line?
Solution. Let the page have $x$ lines, and each line have $y$ letters. From the first condition of the problem, we find the equation

$$
3 x+2(y-3)=145
$$

and from the second, the equation

$$
4 x+3(y+4)=224
$$

Solving the system of equations, composed of equations (1) and (2), we get $x=29$, $y=32$. Therefore, on the mentioned page of the book, there are 29 lines, and each line has 32 letters.