Linear Equations and Inequalities - Applications of Linear Equations in Real Life

A school is organising a class outing. Each student pays the same amount.
The total cost of the outing is \(\$180\). There are \(x\) students in the class. Each student pays \(\$6\).

1. Form an equation in terms of \(x\).
2. Solve the equation to find the number of students.
3. Later, \(5\) more students join the outing, but the total cost remains the same.
   Find the new amount each student has to pay.
4. Explain whether the cost per student increases or decreases, and why.
5. If instead the total cost increases by \(\$30\) while the original number of students remains the same, find the new cost per student.