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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 points)

This problem is for grade 9 students only.

Deadline expired on 10 January 2011.

Google Translation (Sorry, the solution is published in Hungarian only.)

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 on problem K. 274.
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

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