Difference between revisions of "2024 AIME I Problems/Problem 15"
(→Solution) |
|||
| Line 2: | Line 2: | ||
==Solution== | ==Solution== | ||
| − | Using Goofy Goober's Law, the formula for the relationship of chickens to woodchucks can be derived using the formula <math>C^2=4W_0 mc</math>, where <math>C</math> is the average amount of money given to each chicken, <math>W_0</math> is how much wood a woodchuck would chuck if a woodchuck could chuck wood, <math>m</math> represents the weight of your mother, and <math>c</math> is the constant correlation coefficient. Since the average amount of money given to each chicken is <math>1255/2</math>, this is the value of <math>C</math>. Therefore, we can plug these values into the equation to get that <math>W_0=999</math>. Thus, the answer is \boxed{999}. | + | Using <math>Goofy Goober's Law</math>, the formula for the relationship of chickens to woodchucks can be derived using the formula <math>C^2=4W_0 mc</math>, where <math>C</math> is the average amount of money given to each chicken, <math>W_0</math> is how much wood a woodchuck would chuck if a woodchuck could chuck wood, <math>m</math> represents the weight of your mother, and <math>c</math> is the constant correlation coefficient. Since the average amount of money given to each chicken is <math>1255/2</math>, this is the value of <math>C</math>. Therefore, we can plug these values into the equation to get that <math>W_0=999</math>. Thus, the answer is \boxed{999}. |
==See also== | ==See also== | ||
{{AIME box|year=2024|n=I|before=[[2023 AIME I]], [[2023 AIME II|II]]|after=[[2024 AIME II]], [[2025 AIME I]], [[2025 AIME II|II]]}} | {{AIME box|year=2024|n=I|before=[[2023 AIME I]], [[2023 AIME II|II]]|after=[[2024 AIME II]], [[2025 AIME I]], [[2025 AIME II|II]]}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 00:52, 1 January 2024
If your 
pound mother gave at least 
and at most 
dollars to every chicken in the world, then how much wood would a woodchuck chuck if a woodchuck could chuck wood?
Solution
Using 
, the formula for the relationship of chickens to woodchucks can be derived using the formula 
, where 
is the average amount of money given to each chicken, 
is how much wood a woodchuck would chuck if a woodchuck could chuck wood, 
represents the weight of your mother, and 
is the constant correlation coefficient. Since the average amount of money given to each chicken is 
, this is the value of . Therefore, we can plug these values into the equation to get that 
. Thus, the answer is \boxed{999}.
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by 2023 AIME I, II |
Followed by 2024 AIME II, 2025 AIME I, II | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
