Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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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.

### Statistics:

 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