Problem K/C. 722. (February 2022)

K/C. 722. The arithmetic mean of two three-digit numbers equals the number obtained by writing them next to each other, separated by a decimal point. What may be the two numbers?

(5 pont)

Deadline expired on March 10, 2022.

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

Megoldás. \(\displaystyle \frac{A+B}{2} = \overline{A,B} = A + \frac{B}{1000}\), ahonnan \(\displaystyle A+B = 2A + \frac{B}{500}\). Mivel a bal oldal egész, a jobb oldalnak is annak kell lennie, ami csak úgy lehet, ha \(\displaystyle B = 500\). Ekkor \(\displaystyle A+500 = 2A+1\), ahonnan \(\displaystyle A=499\).

Ellenőrzés: \(\displaystyle \frac{499+500}{2}=499,500\).

Statistics:

193 students sent a solution.
5 points:	80 students.
4 points:	67 students.
3 points:	15 students.
2 points:	2 students.
1 point:	3 students.
0 point:	3 students.
Unfair, not evaluated:	10 solutionss.
Not shown because of missing birth date or parental permission:	2 solutions.

Problems in Mathematics of KöMaL, February 2022