A school is comprised of 400 people both teachers and students. If 10

We are given that there are 400 total teachers and students, and that 10% of the people are teachers. Thus, there are 0.1 x 400 = 40 teachers. We are also given that 400 people enter the school, and we need to determine how many of those people must be teachers to decrease the percentage of teachers to 5 percent. We can let t = the number of new teachers and create the following equation:

teachers/total = 5%

(40 + t)/(400 + 400) = 1/20

(40 + t)/800 = 1/20

20(40 + t) = 800

800 + t = 800

t = 0

Alternate Solution:

We currently have a group of 400 individuals, 10% of whom are teachers. We will add 400 additional individuals, whose percentage (p) is unknown. This will result in our having 800 individuals, 5% of whom are teachers. We can summarize this in the following equation:

400(0.10) + 400p = 800(0.05)

40 + 400p = 40

400p = 0

p = 0

The percentage of teachers in the new group is 0%, which means that none of the people in the new group will be teachers.

Answer: E