Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 415. (March 2014)

K. 415. Students played with dice in the maths club. 40% of the dice were red, the rest of them were green. Next time, the number of red dice was increased by 10%, and the number of green dice was reduced by 5%. By what percentage did the number of dice change?

(6 pont)

Deadline expired on April 10, 2014.

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

Megoldás. Az első alkalommal a dobókockák száma legyen $\displaystyle x$. Ekkor $\displaystyle 0,4x$ db piros és $\displaystyle 0,6x$ db zöld dobókocka volt a szakkörön. A másik alkalommal a pirosak száma $\displaystyle 0,1\cdot0,4x$-szel nőtt, a zöldeké pedig $\displaystyle 0,05\cdot0,6x$-szel csökkent. Vagyis $\displaystyle 0,4x + 0,04x + 0,6x – 0,03x = 1,01x$ lett a dobókockák száma, ami 1 %-os változást jelent.

Statistics:

 180 students sent a solution. 6 points: 115 students. 5 points: 36 students. 4 points: 11 students. 3 points: 8 students. 1 point: 1 student. 0 point: 3 students. Unfair, not evaluated: 6 solutionss.

Problems in Mathematics of KöMaL, March 2014