The cost of withdrawing money from an ATM consists of two parts. There is a base fee, which is independent of the amount withdrawn. In addition, there is a part that is directly proportional to the amount withdrawn. What is the cost of withdrawing $85000 \mathrm{Ft}$, if the cost of withdrawing $40000 \mathrm{Ft}$ is $221 \mathrm{Ft}$, and the cost of withdrawing $100000 \mathrm{Ft}$ is $485 \mathrm{Ft}$?
I. solution. Let the base fee be $x$, and the ratio be $y$. The following two equations can be written:

$$
\begin{aligned}
& 221=x+40000 y \\
& 485=x+100000 y
\end{aligned}
$$

Subtracting (1) from (2): $264=60000 y$, from which $y=\frac{11}{2500}$. Substituting this back into (1), the base fee can be expressed as:

$$
x=221-40000 \cdot \frac{11}{2500}=45
$$

Thus, the cost for a loan of 85000 forints is:

$$
x+85000 \cdot y=45+85000 \cdot \frac{11}{2500}=419 \text{ Ft}
$$

II. solution. Let the base fee be $x$. Then the part proportional to the loan amount in the first case is $221-x$, and in the second case it is $485-x$. The ratio of these to their respective loan amounts is the same:

$$
\frac{221-x}{40000}=\frac{485-x}{100000}
$$

From this, $x=45$, and thus the proportional part is $\frac{221-45}{40000}=0.44\%$ of the loan amount. For 85000 Ft, the total cost is:

$$
85000 \cdot 0.0044+45=419 \text{ Ft}
$$