2003 AMC 8 第 4 题

先试着解答 2003 AMC 8 第 4 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2003 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

4.

一群骑自行车和三轮车的孩子经过 Billy Bob 家。Billy Bob 数到 77 个孩子和 1919 个轮子。有多少辆三轮车?
A group of children riding on bicycles and tricycles rode past Billy Bob’s house. Billy Bob counted 77 children and 1919 wheels. How many tricycles were there?
22
44
55
66
77
答案:C
知识点:方程组
小提示:
如果 77 个孩子都骑自行车,先数轮子
If all 77 children had bicycles, count the wheels.
大提示:
每辆三轮车比自行车多一个轮子
Each tricycle adds one wheel compared with a bicycle.
解答:
设 bb 为自行车数量,tt 为三轮车数量。可列方程组:b+t=7,2b+3t=19。 \begin{gather*} b + t = 7, \\ 2b + 3t = 19\text{。} \end{gather*} 将第一个方程乘以 22,再从第二个方程中减去所得等式,得到 t=5t = 5。
所以正确答案是 C。
Let bb be the number of bicycles and tt be the number of tricycles. Then we can set up the following system of equations: b+t=7,2b+3t=19. \begin{gather*} b + t = 7, \\ 2b + 3t = 19. \end{gather*} Multiplying the first equation by 22 and subtracting from the second equation, we get t=5.t = 5.
Thus, C is the correct answer.
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