I need help setting up a story problem with system of equations!

The goal is to find out how many teachers and teacher's aides should be hired in order to minimize salary costs.

The salary for a teacher is $35,000.
The salary for a teacher's aide is $18,000.

There school can have to more than 50 faculty members, and no less than 20.
The school must have at least 12 aides.
The number of teachers must be at least twice the number of aides.

Question

I need help setting up a story problem with system of equations!

The goal is to find out how many teachers and teacher's aides should be hired in order to minimize salary costs.

The salary for a teacher is $35,000.
The salary for a teacher's aide is $18,000.

There school can have to more than 50 faculty members, and no less than 20.
The school must have at least 12 aides.
The number of teachers must be at least twice the number of aides.

farmdawgnation · Answer

Hey, bd3ll. Please stop deleting your own questions. Other users have been trying to help you out.

anonymous · Answer

Sorry, I decided to rewrite it and repost

farmdawgnation · Answer

Ok, I'll take your word for it. But someone was typing on your last post and it got deleted while they were working. So, I just wanted to make sure you had a good reason for deleting. :)

anonymous · Answer

It is no more than 50?

anonymous · Answer

I have these... they look right?
$$x+y \le50$$
$$x+y \ge20$$
$$x \ge12$$
$$2y \ge x$$

anonymous · Answer

x=# of teachers
y=# of teacher's aides

anonymous · Answer

I like using variables names that are easy. In this case, t and a make more sense than x and y.

Yes,
t+a <= 50
t+a >= 20
a >= 12
t >= 2a

anonymous · Answer

To minimize salaries, you need as few people as possible.
So, it seems like picking the minimum aides and minimum teacher to aide ratio seems to do the trick.