Problem K. 243. (February 2010)

K. 243. Grandma makes muffins with two kinds of filling for her grandchildren: jam and cheese. One time, 40% of the muffins she made were filled with jam. Another time she made 10% more with jam filling and 5% less with cheese filling. By what percentage did the number of all muffins change?

(6 pont)

Deadline expired on March 10, 2010.

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

Megoldás. Az első alkalommal készített derelyék száma legyen x. Ekkor 0,4x db lekvárost és 0,6x db túrósat készített. A másik alkalommal a lekvárosok száma \(\displaystyle 0,1 \cdot 0,4x\)-szel nőtt, a túrósoké pedig \(\displaystyle 0,05 \cdot 0,6x\)-szel csökkent. Vagyis \(\displaystyle 0,4x+0,04x+0,6x–0,03x=1,01x\) lett a derelyék száma, azaz 1%-kal növekedett.

Statistics:

171 students sent a solution.
6 points:	144 students.
5 points:	8 students.
4 points:	2 students.
2 points:	11 students.
1 point:	2 students.
0 point:	3 students.
Unfair, not evaluated:	1 solutions.

Problems in Mathematics of KöMaL, February 2010