27. If the team had scored 97 points in the last sport, the average number of points scored by it in one sport would have been 90; if it had scored 73 points in this last sport, the average number of points per sport would have been 87. In how many sports did the team compete?
27. Let the team compete in $x$ sports and score $n$ points in all sports except the last one. Then we have

$$
(97+n): x=90 ;(73+n): x=87
$$

which means $97+n=90 x$ and $73+n=87 x$, so $x=8$.