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Problem 287

AMC 12 late, AIME early

Number theory Difficulty 4.5 Find the answer

8. A certain cargo yard has 2005 vehicles waiting in line to be loaded, with the requirement that the first vehicle must load 9 boxes of cargo, and every 4 adjacent vehicles must load a total of 34 boxes. To meet the above requirements, the minimum number of boxes of cargo should be ( ).
(A) 17043
(B) 17044
(C) 17045
(D) 17046

Your answer

Official solution

8. A.

Except for the first vehicle which carries 9 boxes, among the remaining 2004 vehicles, every 4 vehicles carry 34 boxes, so there are $\frac{2004}{4} \times 34+9=17043$ boxes.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.