Question

I need the 2 equations and the answer I don't have a calculator

Answer 1

We can call:

S: the number of students that assisted to the movies.

A: the number of adults that assited to the movies.

Then, as the total number of assistants is 40 and is the sum of the number of students and the number of adults, we can write:

`S+A=40`

He spent $180, and this expense is the sum of $4 per student, a total of 4*S, and $6 per adult, a total of 6*A, so we can write:

`4S+6A=180`

To solve this, we substitute one of the variables with the information from the first equation and solve the second equation:

`S+A=40\Rightarrow S=40-A`
`\begin{gathered} 4(40-A)+6A=180 \\ 160-4A+6A=180 \\ 160+2A=180 \\ 2A=180-160 \\ 2A=20 \\ A=(20)/(2) \\ A=10 \end{gathered}`

With tha value A=10 (10 adults), we calcualte the numebr of students S as:

`S=40-A=40-10=30`

Answer:

Being S: the number of students, and A: the number of adults,

The first equation is: S+A=40.

The second equation is: 4S+6A=180

The assistants to the movies were 30 students and 10 adults.