Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 591. (September 2018)

K. 591. A group of children participated in a bus excursion. In the luggage compartment of the bus, there is room for the luggage of one third of the children. The bus has 52 seats. The teachers are sitting on two seats. On each of the remaining seats, there is either a child sitting, or there is the luggage of a child. How many children are there on the trip if all seats are used?

(6 pont)

Deadline expired on October 10, 2018.

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

Megoldás. A buszban a gyerekek \(\displaystyle 2/3\) részének hátizsákja foglalt el egy-egy ülést, tehát az elfoglalt helyek összesen a gyerekek számának \(\displaystyle 5/3\) részével egyenlők. Mivel \(\displaystyle 50\) gyereknek lenne hely a buszban, ezért a gyerekek számának \(\displaystyle 5/3\) része \(\displaystyle 50\), azaz a gyerekek száma \(\displaystyle 30\).


301 students sent a solution.
6 points:239 students.
5 points:3 students.
4 points:3 students.
3 points:6 students.
2 points:1 student.
1 point:3 students.
Unfair, not evaluated:1 solutions.
Not shown because of missing birth date or parental permission:45 solutions.

Problems in Mathematics of KöMaL, September 2018