Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 823. (October 2005)

C. 823. On its second birthday, a department store introduced sales prices. Those buying merchandise for more than 50 000 forints (HUF) enjoyed two successive discounts. Both percentage reductions were whole numbers less than 10. A television set that originally cost 69 000 forints was sold for 60 306 forints. Calculate the percentages.

(5 pont)

Deadline expired on November 15, 2005.

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

Megoldás: Legyen p%-os és q%-os a két árengedmény. Ekkor 69000pq=60306, azaz pq=0,874, ami 100p.100q=8740=22.5.19.23 alakban is írható. Tudjuk, hogy 90<100p<100, 90<100q<100. A két szám csak a 92 és 95 (de fordított sorrendben is) lehet, azaz 8 %-os és 5 %-os árengedményeket kaptunk.

Statistics:

 530 students sent a solution. 5 points: 348 students. 4 points: 66 students. 3 points: 20 students. 2 points: 33 students. 1 point: 10 students. 0 point: 31 students. Unfair, not evaluated: 22 solutions.

Problems in Mathematics of KöMaL, October 2005