2016 AMC 10B 第 13 题

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

小提示：

设双胞胎、三胞胎、四胞胎的组数分别为

w,r,q

。

Let

w,r,q

be the numbers of twin, triplet, and quadruplet sets

大提示：

使用

r=4q

和

w=3r

。

Use

r=4q

and

w=3r

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

2w+3r+4q=1000\text{。}

条件给出

r=4q

，且

w=3r=12q

。

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

小提示：

大提示：

解答：

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