Problem K. 675. (December 2020)

K. 675. A large company was giving a Christmas party to its employees. Some of them brought their spouses along. There were five times as many men present at the party as women. At 10 p.m., some husbands left for home with their wives, and thus the number of women dropped to one seventh of the number of men remaining. What fraction of the men left at 10 p.m.?

(6 pont)

Deadline expired on January 11, 2021.

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

Megoldás. Legyen a parti elején a nők száma \(\displaystyle x\), a férfiak száma ekkor \(\displaystyle 5x\). 10 órakor távozott \(\displaystyle y\) házaspár, tehát ez után a férfiak száma \(\displaystyle 5x–y\), a nők száma \(\displaystyle x–y\) lett. A megadott összefüggés alapján \(\displaystyle 5x–y = 7(x–y)\), rendezve \(\displaystyle 2x = 6y\), vagyis \(\displaystyle x=3y\). Tehát a parti elején \(\displaystyle 3y\) nő és \(\displaystyle 15y\) férfi volt jelen, így 10 órakor a férfiak \(\displaystyle 1/15\) része ment haza a feleségével.

Statistics:

115 students sent a solution.
6 points:	78 students.
5 points:	7 students.
4 points:	6 students.
3 points:	3 students.
2 points:	6 students.
1 point:	6 students.
0 point:	3 students.
Unfair, not evaluated:	5 solutionss.
Not shown because of missing birth date or parental permission:	1 solutions.

Problems in Mathematics of KöMaL, December 2020