Problem C. 885. (February 2007)

C. 885. The charge of money withdrawal from an ATM is made up of two terms. There is a flat charge independent of the amount withdrawn and another part that is proportional to it. For forints (Hungarian currency, HUF) withdrawn the charge is 221 forints, and for it is 485 forints. What is the charge for forints?

(5 pont)

Deadline expired on March 19, 2007.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Jelölje az alapdíjat a, az arányt pedig p. Ekkor:

(2)-ből (1)-et kivonva:

264=60000p,

és innen p=0,0044.

Ezt visszaírva (1)-be:

221=a+40000^.0,0044,

ahonnan a=45.

A keresett érték:

45+85000^.0,0044=419.

Tehát 85000 Ft felvétele esetén 419 Ft a költség.

Statistics:

433 students sent a solution.
5 points:	402 students.
4 points:	16 students.
3 points:	5 students.
2 points:	1 student.
1 point:	4 students.
0 point:	4 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, February 2007