Question

There are 5 times as many students as teachers on the field trip and sum of the students or teachers is 132.Find the number of students and teachers.

Answer 1

Students = 110

Teachers = 22

Step-by-step explanation

Let the number of students be s.

Let the number of teachers be t.

There are 5 times as many students as teachers. This means that:

`\begin{gathered} s=5\cdot t \\ s=5t \end{gathered}`

The sum of students and teachers is 132. This means that:

`s+t=132`

We can solve this by substitution. To do this, substitute the first equation into the second.

That is:

`\begin{gathered} 5t+t=132 \\ 6t=132 \\ \text{Divide both sides by 6:} \\ (6t)/(6)=(132)/(6) \\ t=22 \end{gathered}`

Recall that:

`\begin{gathered} s=5t \\ \Rightarrow s=5\cdot22 \\ s=110 \end{gathered}`

Therefore, there are 110 students and 22 teachers.