Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 239. (January 2010)

K. 239. Someone bought a bar of chocolate, and then realised that the same chocolate in another shop cost as many percent more, as the price in forints (HUF, Hungarian currency) that he had paid for it. How much did he pay for the chocolate if it cost 75 forints in the other shop?

(6 pont)

Deadline expired on February 10, 2010.

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

Megoldás. A feladat szerint $\displaystyle 75= x+ \frac{x}{100}\cdot x$. Az egyenletet rendezve

$\displaystyle 7500=100x+x^2,$

amit a másodfokú egyenletek megoldóképletével megoldva $\displaystyle x=\frac{-100\pm \sqrt{10000+4\cdot 1\cdot 7500}}{2}=\frac{-100\pm 200}{2}$. Az egyik megoldás negatív, ami nem lehetséges, a másik megoldás pedig az 50. A csoki eredetileg 50 Ft-ba került.

### Statistics:

 173 students sent a solution. 6 points: 130 students. 5 points: 16 students. 4 points: 3 students. 3 points: 2 students. 2 points: 1 student. 1 point: 16 students. 0 point: 2 students. Unfair, not evaluated: 3 solutions.

Problems in Mathematics of KöMaL, January 2010