Difference between revisions of "2004 AMC 12B Problems/Problem 1"
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| + | == Problem == | ||
Jasmine had <math>2</math> paperclips on Monday, then she had <math>6</math> on Tuesday, and her number of paperclips proceeded to triple on each subsequent day. On what day of the week did she first have more than <math>100</math> paperclips? | Jasmine had <math>2</math> paperclips on Monday, then she had <math>6</math> on Tuesday, and her number of paperclips proceeded to triple on each subsequent day. On what day of the week did she first have more than <math>100</math> paperclips? | ||
| − | ==Solution== | + | == Solution == |
Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made <math>\frac{1}{2} \cdot 48 = 24</math> free throws, on the third <math>12</math>, on the second <math>6</math>, and on the first <math>3 \Rightarrow \mathrm{(A)}</math>. | Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made <math>\frac{1}{2} \cdot 48 = 24</math> free throws, on the third <math>12</math>, on the second <math>6</math>, and on the first <math>3 \Rightarrow \mathrm{(A)}</math>. | ||
Because there are five days, or four transformations between days (day 1 <math>\rightarrow</math> day 2 <math>\rightarrow</math> day 3 <math>\rightarrow</math> day 4 <math>\rightarrow</math> day 5), she makes <math>48 \cdot \frac{1}{2^4} = \boxed{\mathrm{(A)}\ 3}</math> | Because there are five days, or four transformations between days (day 1 <math>\rightarrow</math> day 2 <math>\rightarrow</math> day 3 <math>\rightarrow</math> day 4 <math>\rightarrow</math> day 5), she makes <math>48 \cdot \frac{1}{2^4} = \boxed{\mathrm{(A)}\ 3}</math> | ||
| − | ==See Also== | + | == See Also == |
{{AMC12 box|year=2004|ab=B|before=First Question|num-a=2}} | {{AMC12 box|year=2004|ab=B|before=First Question|num-a=2}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 02:52, 7 January 2021
Problem
Jasmine had 
paperclips on Monday, then she had 
on Tuesday, and her number of paperclips proceeded to triple on each subsequent day. On what day of the week did she first have more than 
paperclips?
Solution
Each day Jenny makes half as many free throws as she does at the next practice. Hence on the fourth day she made 
free throws, on the third 
, on the second , and on the first 
.
Because there are five days, or four transformations between days (day 1 
day 2 day 3 day 4 day 5), she makes 
See Also
| 2004 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. 
