Final answer:
To make 204 pumpkin pies, knowing that three pumpkins yield 9 pies, you simply divide 204 pies by the 3 pies that one pumpkin can produce to get 68. Hence, 68 pumpkins are needed.
Step-by-step explanation:
To find out how many pumpkins are needed to make 204 pumpkin pies, when it is known that three pumpkins make 9 pumpkin pies, we need to establish the rate of pumpkins to pies and then scale this up to the desired number of pies. We start by calculating the number of pies one pumpkin can make by dividing the number of pies by the number of pumpkins, which is 9 pies divided by 3 pumpkins, equaling 3 pies per pumpkin. Once we have this rate, we use it to find out how many pumpkins we need for 204 pies by dividing 204 by 3, which gives us 68 pumpkins. Therefore, 68 pumpkins are needed to make 204 pumpkin pies.