English Információ A lap Pontverseny Cikkek Hírek Fórum

Rendelje meg a KöMaL-t!

VersenyVizsga portál

Kísérletek.hu

Matematika oktatási portál

K. 235. The official currency on the planet Kloppar is the tirof, for which the small change is the dimar, and there is an even smaller change called the nepi. One dimar is worth a whole number of nepis, and a tirof is worth a whole number of dimars. Sangi had dinner in a restaurant on the planet. After dinner he received the following bill: Fried vondar: 7 dimars and 2 nepis; Pickled rotins: 10 dimars and 5 nepis; Vundeg bread: 1 dimar and 6 nepis; Carbonated nestaki drink: 6 dimars and 4 nepis; Krabban cake: 4 dimars; Total: 2 tirofs, 8 dimars and 1 nepi. How many dimars are worth a tirof, and how many nepis are worth a dimar?

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 February 2010.

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

Megoldás. Legyen $\displaystyle x$ dimar 1 tirof és $\displaystyle y$ nepi 1 dimar. Az étlap árai szerint 1 dimar legalább 7 nepi ($\displaystyle y>6$) és 1 tirof legalább 11 dimar ($\displaystyle x>10$). Ekkor a számla összesen $\displaystyle (7y+2)+(10y+5)+(y+6)+(6y+4)+(4y)=28y+17$, másrészről a kifizetett 2 tirof 8 dimar 1 nepi $\displaystyle 2xy+8y+1$. Az egyenlőségükből $\displaystyle 2xy=20y+16$, amiből $\displaystyle x$-t kifejezve $\displaystyle x=\frac{10y+8}{y}=10+\frac 8y$. A kezdeti feltételek miatt $\displaystyle y=8$ és $\displaystyle x=11$, azaz 1 tirof 11 dimar és 1 dimar 8 nepi.

Statistics on problem K. 235.
 172 students sent a solution. 6 points: 77 students. 5 points: 9 students. 4 points: 4 students. 3 points: 38 students. 2 points: 20 students. 1 point: 14 students. 0 point: 7 students. Unfair, not evaluated: 3 solutions.

• Problems in Mathematics of KöMaL, January 2010

•  Támogatóink: Morgan Stanley