AMC 8 1985 Problem 18
AMC8 1985 年第 18 题
特殊数与不定方程★★★☆☆
Nine copies of a certain pamphlet cost less than $10.00 while ten copies of the same pamphlet (at the same price) cost more than $11.00. How much does one copy of this pamphlet cost?
某种小册子九份的价钱低于 $10.00，而同一小册子十份的价钱（相同单价）高于 $11.00。该小册子一份多少钱？
- A.$1.07
- B.$1.08
- C.$1.09
- D.$1.10
- E.$1.11
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Let be the cost of one pamphlet in dollars. The first restriction implies 9p<10, that is, p<1.1111..., while the section restriction implies 10p>11, that is, p>1.10. Thus 1.10 < p < 1.1111..., and thus p = 1.11, since the price must be a whole number of cents.
Note: the second restriction alone eliminates all the incorrect answer choices.
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