Mathematical and Physical Journal
for High Schools
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Problem K. 250. (March 2010)

K. 250. Two people tried to estimate the size of the audience at an open air concert. One of them guessed there were 2700 spectators, the other one guessed 3600. It turned out that one of the percentage errors made was twice the other, but one underestimated and the other overestimated the audience. What may have been the number of spectators at the concert?

(6 pont)

Deadline expired on April 12, 2010.


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

Megoldás. Legyen a kisebbik tévedés \(\displaystyle p \%\). Két eset lehetséges.

I. eset: \(\displaystyle \frac{2700}{1-\frac{p}{100}}=\frac{3600}{1+\frac{2p}{100}}\). Innen \(\displaystyle p=10\), vagyis 3000-en voltak a koncerten.

II. eset: \(\displaystyle \frac{2700}{1-\frac{2p}{100}}=\frac{3600}{1+\frac{p}{100}}\). Innen \(\displaystyle p=\frac{100}{11}\), vagyis 3300-an voltak a koncerten.

A rendelkezésünkre álló adatok alapján mondhatjuk, hogy vagy 3000, vagy 3300 fő lehetett a koncerten.


Statistics:

124 students sent a solution.
6 points:61 students.
5 points:7 students.
4 points:14 students.
3 points:10 students.
2 points:5 students.
0 point:22 students.
Unfair, not evaluated:5 solutions.

Problems in Mathematics of KöMaL, March 2010