Difference between revisions of "2024 AMC 8 Problems/Problem 8"
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Revision as of 13:48, 26 January 2024
Contents
Problem
On Monday Taye has $2. Every day, he either gains $3 or doubles the amount of money he had on the previous day. How many different dollar amounts could Taye have on Thursday, 3 days later?
Solution 1 (BRUTE FORCE)
How many values could be on the first day? Only 
dollars. The second day, you can either add 
dollars, or double, so you can have 
dollars, or 
. For each of these values, you have values for each. For dollars, you have 
dollars or 
, and for dollars, you have dollars or $
. Now, you have values for each of these. For dollars, you have 
dollars or 
, for dollars, you have 
dollars or 
, for dollars, you have dollars or , and for dollars, you have 
dollars or .
$ and $ repeat leaving you with 
different values.
~ cxsmi (minor formatting edits)
Video Solution 1 (easy to digest) by Power Solve
https://youtu.be/16YYti_pDUg?si=5kw0dc_bZwASNiWm&t=121
Video Solution 2 by SpreadTheMathLove
https://www.youtube.com/watch?v=L83DxusGkSY
See Also
| 2024 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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. 
