Problem K. 685. (February 2021)

K. 685. Steve went picking mushrooms. Since he is becoming better and better at spotting mushrooms, this time he found 62 penny bun mushrooms. The average number in his previous mushroom picking trips had been 30, which was thus increased to 32. How many penny bun mushrooms should he have found in order to increase the mean to 33?

(6 pont)

Deadline expired on March 10, 2021.

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

Megoldás. Ha Pisti \(\displaystyle x\) alkalommal volt korábban gombászni, akkor \(\displaystyle 30x\) darab vargányát gyűjtött, a mostani gombászással együtt pedig \(\displaystyle 32(x+1)\)-et. A két mennyiség között a most megtalált \(\displaystyle 62\) vargánya az eltérés, ezért \(\displaystyle 30x+62=32(x+1)\). Innen \(\displaystyle x=15\). Ha az átlaga \(\displaystyle 33\)-ra emelkedett volna, akkor a \(\displaystyle 16\) alkalommal összesen \(\displaystyle 16\cdot33=528\) darab vargányát talált volna, így az első \(\displaystyle 15\) alkalommal talált összesen \(\displaystyle 15\cdot30=450\) vargányához még \(\displaystyle 78\)-at kellett volna gyűjtenie.

Statistics:

112 students sent a solution.
6 points:	99 students.
5 points:	5 students.
4 points:	1 student.
3 points:	1 student.
2 points:	3 students.
Unfair, not evaluated:	1 solutions.
Not shown because of missing birth date or parental permission:	2 solutions.

Problems in Mathematics of KöMaL, February 2021