A bus had a utilization ratio of $322.5 \mathrm{~kg} /$ passenger on its route, meaning that out of the empty bus's weight, this much was attributed to one passenger. On the return trip, 18 more passengers boarded the bus, improving the ratio to $187.5 \mathrm{~kg} /$ passenger. What will the ratio be if 7 more passengers board, and thus all available seats are filled?
Denoting the empty weight of the bus by $M$ and the initial number of passengers by $x$:

$$
M=322.5 x=187.5(x+18)
$$

From this, $x=25, M=8062.5 \text{ kg}$.

After 7 more passengers boarded, there were 50 passengers on the bus - this is therefore the allowed number of passengers - and the utilization ratio: $8062.5 / 50=161.25 \text{ kg}/$ passenger.

Próhle Sarolta (Sopron, Széchenyi I. g. I. o. t.)