Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 136. (October 2007)

K. 136. A school took each of its students to a camp once during the summer. This was organized in two groups of the same number of students. 70% of the boys were in the first group and 80% of the girls were in the second group. What percentage of the students in the first group were boys?

(6 pont)

Deadline expired on November 10, 2007.


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

Megoldás: Jelölje a fiútanulók számát f, a lányokét pedig l. Ekkor az első csoportban 0,7f+0,2l, a másodikban 0,3f+0,8l tanuló vett részt. Mivel a két csoport létszáma egyenlő volt, ezért 0,7f+0,2l=0,3f+0,8l, innen 2f=3l. Az első táborozásban tehát 0,7f+0,2\cdot\frac23f=\frac56f tanuló vett részt, ennek a 0,7f a \frac{21}{25} része, azaz 84%-a volt fiú.


Statistics:

221 students sent a solution.
6 points:165 students.
5 points:5 students.
3 points:19 students.
2 points:4 students.
1 point:9 students.
0 point:17 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, October 2007