Maths Olympiad Prep

Track / Stage 4 / 328 of 340 #588 of 1964

Problem 588

AMC 12 late, AIME early
Combinatorics Difficulty 5.0 Find the answer

99. In the zoo, there are some chickens and rabbits, which have a total of 286 legs. The keeper puts 3 chickens and 2 rabbits in each cage, and in the end, there is only 1 chicken and 1 rabbit left in a cage, so the number of chickens is \qquad.

A number or a short expression. Spacing and $ signs are ignored.

Official solution

Answer: 61

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