2000 AMC 10 Problem 3

Below is the professionally curated solution for Problem 3 of the 2000 AMC 10, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 10 solutions, or check the answer key.

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Concepts:percentage work backwards

Difficulty rating: 960

Each day, Jenny ate $20\%$ of the jellybeans that were in her jar at the beginning of that day. At the end of the second day, $32$ remained. How many jellybeans were in the jar originally?

$40$

$50$

$55$

$60$

$75$

Solution:

Since Jenny eats $20\%$ each day, $80\%$ remain at the end of each day.

If $x$ is the original number, then $(0.8)^2 x = 0.64x = 32,$ so $x = 50.$

Thus, the correct answer is B.

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