Difference between revisions of "1985 AJHSME Problem 18"

(Solution)
(In-depth Solution by BoundlessBrain!=)
 
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<math>\text{(E)}</math> <math>$1.11</math>
 
<math>\text{(E)}</math> <math>$1.11</math>
  
=In-depth Solution by BoundlessBrain!==
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==In-depth Solution by BoundlessBrain!==
 
https://youtu.be/pZdArd1FSYA
 
https://youtu.be/pZdArd1FSYA
  

Latest revision as of 15:03, 4 July 2023

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)} $1.11.}$