Difference between revisions of "1985 AJHSME Problem 18"
Coolmath34 (talk | contribs) (Created page with "== Problem == 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</mat...") |
(→In-depth Solution by BoundlessBrain!=) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 11: | Line 11: | ||
<math>\text{(E)}</math> <math>\$1.11</math> | <math>\text{(E)}</math> <math>\$1.11</math> | ||
| + | |||
| + | ==In-depth Solution by BoundlessBrain!== | ||
| + | https://youtu.be/pZdArd1FSYA | ||
== Solution== | == Solution== | ||
Latest revision as of 15:03, 4 July 2023
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?
In-depth Solution by BoundlessBrain!
Solution
Let the cost of one pamphlet be 
Then we have 
and 
Multiply both inequalities as follows:
![\[9x < 10 \rightarrow 900x < 1000\]](http://latex.artofproblemsolving.com/8/6/7/867e58bb7352b1fcdf095939f18a853c08dd933a.png)
![\[10x > 11 \rightarrow 900x > 990\]](http://latex.artofproblemsolving.com/6/b/4/6b4641e19abf785b49301ba7863024593de9fba2.png)
The only answer choice that satisfies both inequalities is 
