448. A regiment of cuirassiers buys a certain number of horses for 11250 francs. A regiment of dragoons buys fifteen more horses for 16000 francs. Each dragoon horse is 50 francs cheaper than a cuirassier horse. Determine the number of horses of each type and their cost.
448. If there are $x$ cuirassier horses, then there are $x+15$ dragoon horses. The cost of the former is $\frac{11250}{x}$, and the cost of the latter is $\frac{16000}{15+x}$. According to the condition,

$$
\frac{11250}{x}=\frac{16000}{x+15}+50
$$

The authors solve it as follows: after simplification,

$$
x^{2}+110 x=335
$$

they add $55^{2}$ to both sides:

$$
(x+55)^{2}=6400
$$

from which $x=25$.