AMC10 2016 B

AMC10 2016 B · Q13

AMC10 2016 B · Q13. It mainly tests Linear equations, Arithmetic misc.

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 three times as many sets of twins as sets of triplets. How many of these 1000 babies were in sets of quadruplets?

在大都会医院的某一年，多胎出生的统计如下：双胞胎、三胞胎和四胞胎这些组合共占当年出生婴儿中的1000名。三胞胎的组数是四胞胎组数的4倍，双胞胎的组数是三胞胎组数的3倍。在这1000名婴儿中，有多少名属于四胞胎组合？

(A) 25 25

(B) 40 40

(D) 100 100

(E) 160 160

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let $x$ denote the number of sets of quadruplets. Then $1000 = 4\cdot x + 3\cdot (4x) + 2\cdot (3\cdot 4x) = 40x$. Thus $x = 25$, and the number of babies in sets of quadruplets is $4\cdot 25 = 100$.

答案（D）：设 $x$ 表示四胞胎组的数量。则 $1000 = 4\cdot x + 3\cdot (4x) + 2\cdot (3\cdot 4x) = 40x$。因此 $x = 25$，四胞胎中的婴儿数为 $4\cdot 25 = 100$。

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