HMMT 十一月 2018 · 冲刺赛 · 第 9 题

HMMT November 2018 — Guts Round — Problem 9

[ 7 ] Farmer James has some strange animals. His hens have 2 heads and 8 legs, his peacocks have 3 heads and 9 legs, and his zombie hens have 6 heads and 12 legs. Farmer James counts 800 heads and 2018 legs on his farm. What is the number of animals that Farmer James has on his farm? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT November 2018, November 10, 2018 — GUTS ROUND Organization Team Team ID#

解析

[ 7 ] Farmer James has some strange animals. His hens have 2 heads and 8 legs, his peacocks have 3 heads and 9 legs, and his zombie hens have 6 heads and 12 legs. Farmer James counts 800 heads and 2018 legs on his farm. What is the number of animals that Farmer James has on his farm? Proposed by: James Lin Answer: 203 Note that each animal has 6 more legs than heads. Thus, if there are n animals, then there are 6 n more legs than heads in total. There are 2018 800 = 1218 more legs than heads in total, so there are 1218 = 203 animals. 6