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HMMT 二月 2001 · GEN1 赛 · 第 3 题

HMMT February 2001 — GEN1 Round — Problem 3

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. There are some red and blue marbles in a box. We are told that there are twelvemore red marbles than blue marbles, and we experimentally determine that when we picka marble randomly we get a blue marble one quarter of the time. How many marbles are there in the box?
解析

英文解析

  1. There are some red and blue marbles in a box. We are told that there are twelvemore red marbles than blue marbles, and we experimentally determine that when we picka marble randomly we get a blue marble one quarter of the time. How many marbles are there in the box?
    Solution: Call the number of blue marbles x , so the number of red marbles is x + 12
    and the total number of marbles is 2 x + 12. The probability of picking a red marble isx 1 = ⇒ x = 6, so 2 x + 12 = 24 .
    2 x +12 4