Difference between revisions of "1985 AJHSME Problems/Problem 18"

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==Problem==
 
==Problem==
  
Nine copies of a certain pamphlet cost less than <dollar/><math>10.00</math> while ten copies of the same pamphlet (at the same price) cost more than <math>\$ 11.00</math>.  How much does one copy of this pamphlet cost?
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Nine copies of a certain pamphlet cost less than <math>\$ 10.00</math> while ten copies of the same pamphlet (at the same price) cost more than <math>\$ 11.00</math>.  How much does one copy of this pamphlet cost?
  
 
<math>\text{(A)}</math> <math>\$1.07</math>  
 
<math>\text{(A)}</math> <math>\$1.07</math>  

Revision as of 12:40, 30 August 2015

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$

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.

$\boxed{\text{E}}$

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions


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