1974 AMC 12 第 7 题

Question

某镇人口先增加

1{,}200

人，随后新人口数减少了

11\%

。此时人口比增加

1{,}200

人之前少

32

人。该镇原有人口是多少？

A town’s population increased by

1{,}200

people, and then this new population decreased by

11\%.

The town now had

32

less people than it did before the

1{,}200

increase. What is the original population?

1{,}200

11{,}200

9{,}968

10{,}000

以上皆非

none of these

设原有人口为

P

，对

P+1200

应用减少的百分比

Let

P

be the original population and apply the decrease to

P+1200

最终人口既可表示为

0.89(P+1200)

，也可表示为

P-32

The final population is both

0.89(P+1200)

and

P-32

设原有人口为

P

。则

0.89(P+1200)=P-32\text{。}

因此

0.11P=1100

，得到

P=10{,}000

。

因此，正确答案是 D。

Let the original population be

P.

Then

0.89(P+1200)=P-32.

Therefore

0.11P=1100,

giving

P=10{,}000.

Therefore, the correct answer is D.

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