The Broken Eggs A farmer is taking her eggs to market in her cart, but she hits a pothole, which knocks over all the containers of eggs. Though she herself is unhurt, every egg is broken. So she goes to her insurance agent who asks her how many eggs she had. She says that she doesn't remember how many eggs she had, but she remembers some things about trying to pack them up. She says that when she packed them in groups of two, there was one egg left over. When she packed them in groups of three, there was also one left over. There was one egg left over when she packed them in groups of four, five and six as well. But when she packed them in groups of seven, she ended up with complete groups and no leftovers. She knows she had more than 500, but less than 1000 eggs. How many eggs did she have?Extension: Suppose that instead of knowing she had between 500 and 1000 eggs, she actually had no idea how many eggs she had. What are other possibilities for the amount of eggs she had? Generalization: What is an equation that you can write to represent the number of eggs the farmer could possiblly have?Another egg problem: Packing up a different group of eggs, the farmer noticed that when she packed the eggs in groups of 3, 5, and 7 there would be one left over. But when packed in groups of 8, there were no left overs. If the number of eggs is between 500 and 1000, how many eggs are there