2021 AMC 10B Spring Problem 3

Question

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

Let the numbers of juniors and seniors be variables

The equal debate-team counts give a second equation

Click to load, then click again to play

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 .

Problem 3 in other years