Question

In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2. When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 4:1. How many students are in the class after these changes?

Answer 1

Let's call the current number of juniors "3x" and the current number of seniors "2x" (since the ratio of juniors to seniors is 3:2).

After six more juniors join, we will have "3x + 6" juniors. And if one senior drops, we will have "2x - 1" seniors.

Now we're told that the new ratio of juniors to seniors is 4:1. This means that the number of juniors is four times the number of seniors. So:

3x + 6 = 4(2x - 1)

Expand the right side:

3x + 6 = 8x - 4

Subtract 3x from both sides:

6 = 5x - 4

Add 4 to both sides:

10 = 5x

Divide both sides by 5:

x = 2

So currently there are 3x = 6 juniors and 2x = 4 seniors.

After the changes, there will be 3x + 6 = 3(2) + 6 = 12 juniors and 2x - 1 = 4 - 1 = 3 seniors.

Altogether, there will be 12 + 3 = 15 students in the class after these changes.