Problem

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?

$\text{(A)}$ $$1.07$

$\text{(B)}$ $$1.08$

$\text{(C)}$ $$1.09$

$\text{(D)}$ $$1.10$

$\text{(E)}$ $$1.11$

In-depth Solution by BoundlessBrain!=

https://youtu.be/pZdArd1FSYA

Solution

Let the cost of one pamphlet be $x.$ Then we have $9x < 10$ and $10x > 11.$ Multiply both inequalities as follows: $9x < 10 \rightarrow 900x < 1000$ $10x > 11 \rightarrow 900x > 990$ The only answer choice that satisfies both inequalities is $\boxed{\text{(E)} $1.11.}$

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1985 AJHSME Problem 18

Problem

In-depth Solution by BoundlessBrain!=

Solution