Problem K/C. 777. (September 2023)

K/C. 777. The arithmetic mean of the numbers \(\displaystyle a\) and \(\displaystyle b\) is 10, the arithmetic mean of \(\displaystyle b\) and 10 is \(\displaystyle c/2\). What is the arithmetic mean of \(\displaystyle a\) and \(\displaystyle c\)?

(5 pont)

Deadline expired on October 10, 2023.

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

Megoldás. \(\displaystyle (a + b)/2 = 10\), \(\displaystyle (b + 10)/2 = c/2\), az elsőből \(\displaystyle a = 20 - b\), a másodikból \(\displaystyle c = b + 10\), ezért \(\displaystyle (a + c)/2 = (20 - b + b + 10) / 2 = 15\).

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Problems in Mathematics of KöMaL, September 2023