13.065. 108 examinees wrote an essay. They were given 480 sheets of paper, with each girl receiving one sheet more than each boy, and all the girls received as many sheets as all the boys. How many girls and how many boys were there?
Solution.

Let $x$ be the number of girls, and $108-x$ be the number of boys. Boys received $y$ sheets each, and girls received $y+1$ sheets each. According to the problem,

$\left\{\begin{array}{l}x(y+1)+(108-x) y=480, \\ x(y+1)=(108-x) y,\end{array}\right.$ from which $x=48$. There were 48 girls and $108-48=60$ boys.

Answer: 48 and 60.