Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 716. (January 2022)

K. 716. In a shop, three notebooks and two pens cost 1110 forints (HUF, Hungarian currency). Five notebooks and four pens cost 2010 forints. What is the price of one notebook, and what is the price of one pen?

(5 pont)

Deadline expired on February 10, 2022.


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

Megoldás. \(\displaystyle 3F+2T=1110\) és \(\displaystyle 5F+4T=2010\). Így \(\displaystyle 6F+4T=2220\), azaz \(\displaystyle F=2220-2010=210\) és így \(\displaystyle 2T=1110-3F=110-3\cdot210=480\) miatt \(\displaystyle T=240\). A füzet ára 210 Ft, a toll ára pedig 240 Ft. Ellenőrzés: \(\displaystyle 3\cdot210+2\cdot240=1110\), \(\displaystyle 5\cdot210+4\cdot240=2010\).


Statistics:

119 students sent a solution.
5 points:111 students.
4 points:3 students.
2 points:1 student.
Unfair, not evaluated:3 solutionss.
Not shown because of missing birth date or parental permission:1 solutions.

Problems in Mathematics of KöMaL, January 2022