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 | + | 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>\dollar 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 11:38, 30 August 2015
Problem
Nine copies of a certain pamphlet cost less than <dollar/>
while ten copies of the same pamphlet (at the same price) cost more than $\dollar 11.00$ (Error compiling LaTeX. Unknown error_msg). How much does one copy of this pamphlet cost?
Solution
Let 
be the cost of the first pamphlet, in dollars. The first part tells us ![\[9p<10 \Rightarrow p<1.\overline{1}\]](http://latex.artofproblemsolving.com/5/5/7/557af92947e952fae9d8684c69e2c81d241ece1b.png)
The second part tells us that ![\[10p>11\Rightarrow p>1.1\]](http://latex.artofproblemsolving.com/5/0/6/5069bd86315ca61578710d54c7b0fa9df324f950.png)
Combining these two parts, the only possible value for is 
, since represents a monetary value.
See Also
| 1985 AJHSME (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
