The residents of a boarding house have to pay their rent. If each of them pays $10 \mathrm{Ft}$, there is a shortage of $88 \mathrm{Ft}$ in the rent, but if each of them pays $10.80 \mathrm{Ft}$, then $2.5 \%$ more money is collected than the rent of the boarding house. How much should each resident pay so that exactly the required amount is collected?
I. Solution: Let the number of residents be denoted by $x$, then the rent for the accommodation is $10 x+88 \mathrm{Ft}$, so the total amount of the increased contributions can be expressed in two ways, and from the equality of the two values,

$$
10.80 x=(100+2.5) \frac{10 x+88}{100}
$$

From this,

$$
x=\frac{90.2}{0.55}=164
$$

and the rent to be paid by each resident:

$$
\frac{10 x+88}{x}=10+\frac{88}{x}=10+\frac{88}{164} \approx 10.54 \mathrm{Ft}
$$

Ilona Kerényi (Debrecen, Kossuth L. Practical Grammar School I. o. t.)

II. Solution: The problem contains more data than necessary to answer the question. That there is a 2.5% overpayment in the second case means - due to the equality of contributions - that this applies to each resident separately, i.e., $10.80 \mathrm{Ft}$ is 102.5% of the rent per resident, so the rent is $10.80: 1.025=10.54 \mathrm{Ft}$.

Ilona Vigh (Szolnok, Verseghy F. Grammar School I. o. t.)