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 solutions.

Problems in Mathematics of KöMaL, March 2014