Thread: system of inequalities

THe Quetion:

The science club can spend at most $400 on a field trip to a dinosaur exhibit. It has enough chaperones to allow at most 100 students to go on the trip. The exhibit costs $3 for students 12 years and younger and $6 for students over 12.

Problem:

Write a system of linear ineqalities to model this situation.

AND

Graph your system of ineqalities. Be sure it is clear which region shows the solution.

Thanks so much!!!

Eeyore11

Originally Posted by eeyore11

THe Quetion:

The science club can spend at most $400 on a field trip to a dinosaur exhibit. It has enough chaperones to allow at most 100 students to go on the trip. The exhibit costs $3 for students 12 years and younger and $6 for students over 12.

Let x variable represent the amount of younger students.
Let y varialbe represent the amount of older students.

Then, x+y <= 100

Each x costs $3 thus in total 3x dollars.
Each y costs $6 thus in total 6y dollars.
The net total is, 3x+6y.
Then, 3x+6y<=400

This yields two inequalities,
x+y<=100
3x+6y<=400

But there are two more, x>=0 and y>=0
These are natural inequalities.
Since you cannot have a negative amount of students going.

So we really have,
x+y<=100
3x+6y<=400
x>=0 and y>=0