Question

There are 6000 students at Mountain High School, and 1/4 of these students are seniors. If 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students (not seniors) are also in favor of forming a debate team how many students do not favor this idea?

Answer 1

hello

tp solve this question, let's get the data out

we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school

the number of senior students are

`(1)/(4)*6000=1500`

we have 1500 seniors in the school.

we can find the seniors in support of a debate team by multiplying 2/3 by 1500

`(2)/(3)*1500=1000`

now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.

`1500-1000=500`

500 seniors from the school are not in support of a debate team.

Also note that 1/5 of the remaining students are not in support of the debate team.

which would be

`\begin{gathered} 6000-1500=4500 \\ (1)/(5)*4500=900 \end{gathered}`

now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team

`500+900=1400`

from the calculationabove, a total of 1400 students are not in support of the idea