Sec 2 E Math Linear Inequalities Q15 - Alternative purchases from a fixed budget

An activity coordinator has a certain budget to buy entry passes. She can either buy exactly \(x\) adult passes at $4.50 each or \((x+5)\) student passes at $3.70 each and have $1.50 left.

1. Form an equation in \(x\) and show that \(x=25\).
2. How much is the coordinator's budget?
3. If the coordinator buys 8 adult passes and uses the rest of the money to buy student passes, find
   1. the maximum number of student passes that she can buy;
   2. the amount of money left.