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K. 55. There are two milk bars in Cowton, and both of them have hot chocolate with frothed chocolate topping on their menus. Each milk bar serves in a cylindrical glass of the same height. (On serving, one half of the volume of the drink is liquid chocolate, and the other half is frothed chocolate.) In a short time, the froth turns into liquid chocolate of one quarter as much volume. In the Jolly Cowboy, chocolate is served in glasses of radius 6 cm, and sold for 12 Cowton cents a glass. In the Happy Cowgirl, the radius of the glasses is 5 cm, but they fill up the glass again when the froth of the first filling has settled. They charge 11 Cowton cents for a glass. In which milk bar is chocolate cheaper? [To obtain the volume of a cylinder, the area of its base is multiplied by its height.] (Based on a problem of the 24th József Öveges Memorial Competition)

(6 points)

This problem is for grade 9 students only.

Deadline expired on 12 December 2005.

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

Megoldás: A Víg Tehénpásztorban a bögre térfogatának része a kapott kakaó mennyisége. A Jókedvű Csordásban a bögre térfogatának része a kapott kakaó mennyisége. Legyen a bögrék magassága h cm! A Víg Tehénpásztorban a bögre térfogata köbcentiméterben mérve 36.h, a kakaó mennyisége pedig , egy petákért köbcenti jár. A Jókedvű Csordásban a bögre térfogata köbcentiméterben mérve 25.h, a kakaó mennyisége pedig , egy petákért köbcenti jár. Mivel , ezért a Jókedvű Csordásban olcsóbb a kakaó.

Statistics on problem K. 55.
 231 students sent a solution. 6 points: 133 students. 5 points: 17 students. 4 points: 25 students. 3 points: 11 students. 2 points: 14 students. 1 point: 8 students. 0 point: 22 students. Unfair, not evaluated: 1 solution.

• Problems in Mathematics of KöMaL, November 2005

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