Problem K. 589. (September 2018)

K. 589. A company regularly hires the same man to mow a certain grassy area. In addition to the labour cost, the man charges a call-out fee of 5000 forints (HUF, Hungarian currency). If he mows the grass three times a month, the labour cost is 1.8 times as much per occasion as it is in the case when he mows the grass four times a month, since in the former case the grass will grow higher which requires more work. On the whole, it is more economical for the company to have the grass mowed four times a month. What is the minimum possible labour cost per mowing in the case of 4 occasions a month, given that it is an integer multiple of 100 forints?

(6 pont)

Deadline expired on October 10, 2018.

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

Megoldás. Legyen \(\displaystyle x\) Ft a havi négy nyírás esetén az alkalmankénti munkadíj. Ekkor \(\displaystyle 15000+3\cdot1,8\cdot x > 20000+4\cdot x\), innen \(\displaystyle 1,4\cdot x>5000\), amiből \(\displaystyle x>3571\). Tehát az alkalmankénti munkadíj havi négy nyírás esetén legalább \(\displaystyle 3600\) Ft.

Statistics:

236 students sent a solution.
6 points:	153 students.
5 points:	30 students.
4 points:	10 students.
3 points:	1 student.
1 point:	4 students.
0 point:	2 students.
Unfair, not evaluated:	3 solutionss.
Not shown because of missing birth date or parental permission:	33 solutions.

Problems in Mathematics of KöMaL, September 2018