Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 274. (December 2010)

K. 274. In a city, 2/3 of the men and 3/5 of the women are married. (Everyone has one spouse and the spouses live in the same city.) What fraction of the inhabitants of the city are married?

(6 pont)

Deadline expired on January 10, 2011.


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

Megoldás. A városban élő férfiak száma legyen \(\displaystyle f\), a nőké \(\displaystyle n\). A házaspárok száma \(\displaystyle \frac 23 f=\frac 35 n\), azaz \(\displaystyle f=\frac9{10}n\). A városban összesen \(\displaystyle f+n=\frac{19}{10}n\)-en élnek, közülük összesen \(\displaystyle 2\cdot \frac 35 n=\frac 65 n\)-en házasságban. Ezért \(\displaystyle \frac 65 : \frac{19}{10}=\mathbf{ \frac{12}{19}}\)-ed része él a lakosságnak házasságban.


Statistics:

221 students sent a solution.
6 points:134 students.
5 points:8 students.
4 points:3 students.
3 points:32 students.
2 points:9 students.
1 point:5 students.
0 point:23 students.
Unfair, not evaluated:7 solutions.

Problems in Mathematics of KöMaL, December 2010