1985 AMC 8 Problem 18

Below is the professionally curated solution for Problem 18 of the 1985 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1985 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:inequality bounding to limit cases

Difficulty rating: 950

18.

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?

$1.07

$1.08

$1.09

$1.10

$1.11

Solution:

From $9p \lt 10$ we get $p \lt 1.111\ldots,$ and from $10p \gt 11$ we get $p \gt 1.10.$

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

Thus, the correct answer is E .

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