1985 AMC 8 第 18 题

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18.

某种小册子九本的总价不到 $10.0010.00,而十本的总价超过 $11.0011.00。一本小册子的价格是多少?

Nine copies of a certain pamphlet cost less than $10.0010.00 while ten copies of the same pamphlet (at the same price) cost more than $11.00.11.00. How much does one copy of this pamphlet cost?

$1.07

$1.08

$1.09

$1.10

$1.11

答案:E
知识点:不等式极限情形界定
难度评级:950
解答:

9p<109p \lt 10p<1.111p \lt 1.111\ldots,由 10p>1110p \gt 11p>1.10p \gt 1.10

$1.10\$1.10$1.111\$1.111\ldots 之间唯一的整美分价格是 $1.11\$1.11

所以正确答案是 E

From 9p<109p \lt 10 we get p<1.111,p \lt 1.111\ldots, and from 10p>1110p \gt 11 we get p>1.10.p \gt 1.10.

The only price in whole cents between $1.10\$1.10 and $1.111\$1.111\ldots is $1.11.\$1.11.

Thus, the correct answer is E .

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