Problem K. 417. (March 2014)

K. 417. A confectioner's shop sells four kinds of cakes: cheese, walnut, poppy seed and chocolate. The number of cakes on stock is 162 without the cheese cakes, 158 without the walnut cakes, 150 without the poppy seed cakes, and 160 without the chocolate cakes. How many cakes of each kind are there on stock?

(6 pont)

Deadline expired on April 10, 2014.

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

Megoldás. A túrós sütik száma legyen \(\displaystyle t\), a diósoké \(\displaystyle d\), a mákosaké \(\displaystyle m\) és a csokisoké \(\displaystyle c\). A következőket tudjuk: \(\displaystyle d + m + c = 162\), \(\displaystyle t + m + c = 158\), \(\displaystyle t + d + c = 150\), \(\displaystyle t + d + m = 160\). Ezek összege: \(\displaystyle 3t + 3d + 3m + 3c = 630\), azaz összesen 630/3=210 sütemény van. Így külön-külön a darabszám: \(\displaystyle t=48\), \(\displaystyle d=52\), \(\displaystyle m=60\), \(\displaystyle c=50\).

Statistics:

184 students sent a solution.
6 points:	168 students.
5 points:	7 students.
4 points:	1 student.
3 points:	5 students.
2 points:	3 students.

Problems in Mathematics of KöMaL, March 2014