Çözüldü Inequality - Natural Numbers (8th Grade)

There are twenty-two pencils in a box, colored blue, red, and black. If the probability of randomly picking a red pencil is greater than that of picking a blue pencil but less than that of picking a black pencil, what is the ratio of the maximum possible number of red pencils to the maximum possible number of blue pencils?

A) 8 / 5
B) 7 / 4
C) 5 / 3
D) 3 / 2

Solution by Google Gemini AI:
Valid quantities B < R < K and B + R + K = 22: 30 different combinations exist.
Maximum red pencils (R): 10 (in the configuration (B = 1, R = 10, K = 11)).
Maximum blue pencils (B): 6 (in the configuration (B = 6, R = 7, K = 9)).
Ratio of these maximums: 10 / 6 = 5 / 3.

Note: The original question (Turkish) that asks for only the maximum number of blue pencils with the choices A) 7, B) 6, C) 5, D) 4
"Hafta Hafta ÖLÇÜM NOKTASI Matematik", Bilfen Yayıncılık, Aralık Deneme Sınavı, Soru 19