Step 1 :Represent the problem with the following equations: \(4c + 8t = 89\) and \(2c + 3t = 34\), where c is the cost of each chair and t is the cost of each table.
Step 2 :Solve this system of equations to find the values of c and t.
Step 3 :The solution to the system of equations gives the cost of each chair and each table. The cost of each chair is \(\frac{5}{4}\) dollars and the cost of each table is \(\frac{21}{2}\) dollars.
Step 4 :Final Answer: The cost to rent each chair is \(\boxed{\$1.25}\) and the cost to rent each table is \(\boxed{\$10.50}\).