A village cart driver usually transports his neighbor to the nearby town for 20 forints, for which he is paid with eggs, which are calculated at 1.60 forints each. At the last monthly settlement, the cart driver received 44 forints. How many rides were there and how many eggs did the cart driver receive in the question month, if the number of eggs did not reach ten times the number of rides, but exceeded nine times the number of rides?
Let the number of carts be denoted by $x$, and the number of eggs by $y$. According to the problem,

$$
20 x-\frac{8}{5} y=44, \quad 9 x<y<10 x
$$

Multiplying our equation by $\frac{5}{4}$,

$$
25 x-2 y=55
$$

from which we get

$$
y=\frac{25 x-55}{2}=12 x-27+\frac{x-1}{2}=12 x-27+u
$$

where

$$
x=2 u+1
$$

Substituting back,

$$
y=24 u+12-27+u=25 u-15
$$

According to the condition,

$$
18 u+9<25 u-15<20 u+10
$$

from which, on one hand,

$$
24<7 u, \quad \text { or } \quad \frac{24}{7}<u
$$

and on the other hand,

$$
5 u<25, \quad \text { or } \quad u<5
$$

These two inequalities are only satisfied by $u=4$, and thus

$$
x=2 u+1=9, \quad y=25 u-15=85
$$

Závody Albin (Győr, 22. sz. gépip. techn. II. o. t.)