2024 RI H1 Q1

The ticket prices for a particular concert were categorised as Cat \(A\) (VIP seated), Cat \(B\) (gallery seated) and Cat \(C\) (gallery standing). After checking with his friends, Olaf discovered the following facts:

The cost of \(5\) Cat \(A\), \(6\) Cat \(B\) and \(9\) Cat \(C\) tickets is \(\$5885\).
A Cat \(B\) ticket costs \(\$70\) more than a Cat \(C\) ticket.
The cost of \(2\) Cat \(B\) tickets and \(3\) Cat \(C\) tickets is equal to the cost of \(2\) Cat \(A\) tickets.

1. Write this information as three linear equations, and hence find the cost of a Cat \(A\) ticket.[4]

During a flash sale, bundles of tickets, each consisting of \(1\) Cat \(A\) and \(2\) Cat \(C\) tickets, are sold at a discount of \(26\%\).

2. If Olaf has \(\$6000\) in his account, what is the maximum number of bundles he can buy?[2]