2021 AMC 10B Spring Problem 3

Below is the video solution and professionally curated solution for Problem 3 of the 2021 AMC 10B Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10B Spring solutions, or check the answer key.

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Concepts:percentage system of equations

Difficulty rating: 870

In an after-school program for juniors and seniors, there is a debate team with an equal number of students from each class on the team. Among the $28$ students in the program, $25\%$ of the juniors and $10\%$ of the seniors are on the debate team. How many juniors are in the program?

$5$

$6$

$8$

$11$

$20$

Video solution:

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Written solution:

Let the number of juniors be $j$ and the number of seniors be $s.$ Then, $j+s = 28$ and $0.25j = 0.1s.$ This means $2.5j = s,$ so $3.5j = 28.$ This makes $j=8.$

Thus, the correct answer is C .

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