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