Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 54. (October 2005)

K. 54. A printing press is working on a board game that uses two kinds of figures moving on the board: dogs and cats. The dog and cat figures are to be cut out of cardboard. The cat to dog ratio in the set of figures packed in the box with each game is 5:3. To reduce wastes, the figures are printed on large sheets of cardboard in two different arrangements. One type of sheet contains 28 dogs and 28 cats, and the other one contains 42 cats. In what proportion should the two types of sheets printed in order to obtain them in the right proportion after cutting out?

(6 pont)

Deadline expired on November 10, 2005.

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

Megoldás: Legyen a vegyes lapból kinyomtatott példányszám x, a csak macskás lapból kinyomtatott példányszám y. Ekkor a keletkező kutyák száma 28x, a keletkező macskák száma pedig 28x+42y. A két állatfigura számának aránya 5:3, tehát {28x+42y\over28x}={5\over3}, innen kis átalakításokkal {x\over y}={9\over4}. Tehát a kívánt darabszámok eléréséhez a vegyes és csak macskás kinyomtatott lapok számának helyes aránya 9:4.


210 students sent a solution.
6 points:139 students.
5 points:9 students.
4 points:6 students.
3 points:4 students.
2 points:5 students.
1 point:32 students.
0 point:14 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, October 2005