One day many years ago, while Farmer Mead was plowing her fields, she came upon an old bottle in the dirt. As she picked it up and and began to brush the dirt off, out came the Math Genie. He offered a crisp new $100 bill to Farmer Mead, as long as she promised to spend the entire $100, and no more, to purchase exactly 100 farm animals. She was to buy at least one cow, one sheep and one horse.
When she arrived at the market, she discovered that sheep cost $0.50 each, horses cost $10.00 each and cows cost $1.00 each. "Wow," she thought, "this is going to be harder than I thought."
Can you help the farmer solve her dilemma? Find a way for Farmer Mead to spend the $100.
Be sure to explain how you solved the problem and how you know your solution is correct.
Extra: Find all the possible ways Farmer Mead could spend the $100 and satisfy the Genie's requirements. Explain how you know you have found them all.