Question

某年 Megapolis 医院的多胞胎统计如下：双胞胎、三胞胎、四胞胎一共占 $1000$ 个出生婴儿。三胞胎组数是四胞胎组数的四倍，双胞胎组数是三胞胎组数的三倍。这 $1000$ 个婴儿中，有多少个属于四胞胎？

At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there were three times as many sets of twins as sets of triplets. How many of these $1000$ babies were in sets of quadruplets?

$\ 25$

$\ 40$

$\ 64$

$\ 100$

$\ 160$

答案：D

知识点：方程组

难度评级：1140

解答：

设双胞胎、三胞胎、四胞胎的组数分别为 $w,r,q$ 。婴儿总数给出条件给出 $r=4q$ ，且 $w=3r=12q$ 。 $2w+3r+4q=1000.$

代入得 $2(12q)+3(4q)+4q$ $=40q=1000$ ，所以 $q=25$ 。四胞胎中的婴儿数为 $4q=100$ 。

所以正确答案是 D。

Let $w,r,q$ be the numbers of sets of twins, triplets, and quadruplets. Then $2w+3r+4q=1000.$ The statement gives $r=4q$ and $w=3r=12q$ .

Substituting gives $2(12q)+3(4q)+4q$ $=40q=1000$ , so $q=25$ . The number of babies in sets of quadruplets is $4q=100$ .

Thus, the correct answer is D.

2016 AMC 10B 第 13 题

答案：D

难度评级：1140

解答：

其他年份的第 13 题