Difference between revisions of "1985 AJHSME Problems/Problem 18"
5849206328x (talk | contribs) (New page: ==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 <dollar/><math>11.00</mat...) |
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==Problem== | ==Problem== | ||
| − | Nine copies of a certain pamphlet cost less than | + | 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>\text{(A)}</math> <math>\$1.07</math> |
| − | <math>\text{(B)}</math | + | <math>\text{(B)}</math> <math>\$1.08</math> |
| − | <math>\text{(C)}</math | + | <math>\text{(C)}</math> <math>\$1.09</math> |
| − | <math>\text{(D)}</math | + | <math>\text{(D)}</math> <math>\$1.10</math> |
| − | <math>\text{(E)}</math | + | <math>\text{(E)}</math> <math>\$1.11</math> |
==Solution== | ==Solution== | ||
| Line 22: | Line 22: | ||
<math>\boxed{\text{E}}</math> | <math>\boxed{\text{E}}</math> | ||
| + | |||
| + | Also, just by quickly going over the answers, it is seen that all of the answers satisfy the first statement: The cost of 9 pamphlet is less that 10 dollars. | ||
| + | |||
| + | The second statement states that 10 pamphlets cost more than 11 dollars. Therefore, since there are only two statements and the first one can be satisfied with all of the answer choices, the answer choice that is the most expensive of them all will be the right answer choice, thus the answer is <math>\boxed{\text{E}}</math> | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/zMt-JeI-KhA | ||
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1985|num-b=17|num-a=19}} |
| + | [[Category:Introductory Algebra Problems]] | ||
| + | |||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 08:03, 22 January 2023
Contents
Problem
Nine copies of a certain pamphlet cost less than 
while ten copies of the same pamphlet (at the same price) cost more than 
. 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.
Also, just by quickly going over the answers, it is seen that all of the answers satisfy the first statement: The cost of 9 pamphlet is less that 10 dollars.
The second statement states that 10 pamphlets cost more than 11 dollars. Therefore, since there are only two statements and the first one can be satisfied with all of the answer choices, the answer choice that is the most expensive of them all will be the right answer choice, thus the answer is
Video Solution
~savannahsolver
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. 
