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HMMT 二月 2001 · GEN1 赛 · 第 4 题

HMMT February 2001 — GEN1 Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find a + b + c + d + e if 3 a + 2 b + 4 d = 10, 6 a + 5 b + 4 c + 3 d + 2 e = 8, a + b + 2 c + 5 e = 3, 2 c + 3 d + 3 e = 4, and a + 2 b + 3 c + d = 7. 6
解析
  1. Find a + b + c + d + e if 3 a + 2 b + 4 d = 10, 6 a + 5 b + 4 c + 3 d + 2 e = 8, a + b + 2 c + 5 e = 3, 2 c + 3 d + 3 e = 4, and a + 2 b + 3 c + d = 7. Solution: Adding the first, third, and fifth equations, we get 5 a + 5 b + 5 c + 5 d + 5 e = 10 + 3 + 7 ⇒ a + b + c + d + e = 4 . 6