Difference between revisions of "2024 AIME I Problems/Problem 15"

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-If your <math>400</math> pound mother gave at least <math>1</math> and at most <math>1254</math> dollars to every chicken in the world, then how much wood would a woodchuck chuck if a woodchuck could chuck wood?
-==Solution==
-Using the EXTREMELY well-known <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 catastrophic 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 <math>\boxed{999}</math>.
-==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]]}}
-{{MAA Notice}}

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