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