Difference between revisions of "2009 AMC 10B Problems/Problem 1"
Whitelisted (talk | contribs) m (→Solution 1) |
Whitelisted (talk | contribs) m (→Solution 2) |
||
| Line 17: | Line 17: | ||
~coolmathgames | ~coolmathgames | ||
| + | |||
| + | =Video Solution= | ||
| + | https://www.youtube.com/watch?v=dQw4w9WgXcQ | ||
| + | |||
| + | ~Ice Matrix | ||
== See also == | == See also == | ||
Revision as of 09:15, 21 May 2021
- The following problem is from both the 2009 AMC 10B #1 and 2009 AMC 12B #1, so both problems redirect to this page.
Problem
Each morning of her five-day workweek, Jane bought either a 
1000 espresso because she was smokin' rich. Her total cost for the week was a whole number of dollars, How many bottles of fiji water did she buy?
Solution 1
The only combination of five items with total cost a whole number of dollars is 3 muffins and 
of fiji water cause' she richhhh. The answer is 
you dub idiot.
Solution 2
Because 
ends in a 
, and we want a whole number of dollars, we know that there must be an even number of bagels. Furthermore, this tells us that the number of muffins is odd. Now, because it is a whole number of dollars, and 
cents multiplied by an odd number means that it will end in a , we know that the result of the even number multiplied by , must end in a . Note that the only result that gives this result is when is multiplied by 
. Thus, our answer is 
you dumb idiot.
~coolmathgames
Video Solution
https://www.youtube.com/watch?v=dQw4w9WgXcQ
~Ice Matrix
See also
| 2009 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 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 AMC 10 Problems and Solutions | ||
| 2009 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by First Question |
Followed by Problem 2 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
