1985 AJHSME Problems/Problem 18

Problem

Nine copies of a certain pamphlet cost less than <dollar/> $10.00$ while ten copies of the same pamphlet (at the same price) cost more than <dollar/> $11.00$ . How much does one copy of this pamphlet cost?

$\text{(A)}$ <dollar/> $1.07$

$\text{(B)}$ <dollar/> $1.08$

$\text{(C)}$ <dollar/> $1.09$

$\text{(D)}$ <dollar/> $1.10$

$\text{(E)}$ <dollar/> $1.11$

Solution

Let $p$ be the cost of the first pamphlet, in dollars. The first part tells us $9p<10 \Rightarrow p<1.\overline{1}$

The second part tells us that $10p>11\Rightarrow p>1.1$

Combining these two parts, the only possible value for $p$ is $1.11$ , since $p$ represents a monetary value.

$\boxed{\text{E}}$

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1985 AJHSME Problems/Problem 18

Problem

Solution

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