Mathematical and Physical Journal
for High Schools
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Problem K. 143. (November 2007)

K. 143. Tickets cost 1500 forints a piece in a cinema, but few people bought them for so much. When the managers decided to reduce the price, the average number of spectators per day increased by 50%, while the total daily income increased by 25%. What was the reduced price of a ticket?

(6 pont)

Deadline expired on December 10, 2007.

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

Megoldás: Jelölje x az eredeti átlagos nézőszámot, az új jegy árát pedig A. A feladat szövege szerint az új átlagos nézőszám x.1,5. Tudjuk, hogy a bevétel=nézőszám.ár. Ez alapján (x.1,5).A=x.1500.1,25, ahonnan A=1500.1,25:1,5=1250. Tehát a jegy árát 1250 Ft-ra csökkentették.


218 students sent a solution.
6 points:116 students.
5 points:36 students.
4 points:13 students.
3 points:13 students.
2 points:17 students.
1 point:11 students.
0 point:7 students.
Unfair, not evaluated:5 solutions.

Problems in Mathematics of KöMaL, November 2007