Welcome to the famous chicken-rabbit cage problem! This is a classic puzzle that helps us practice logical thinking. In our cage, we can count 35 heads total and 94 legs total. Since each animal has exactly one head, we know there are 35 animals. But chickens have 2 legs while rabbits have 4 legs. Can you figure out how many of each animal we have?
Let's solve this step by step using the 'all chickens' method. First, we pretend all 35 animals are chickens. If they were all chickens, we would have 35 times 2 equals 70 legs total. But we actually counted 94 legs! That means we have 24 extra legs. Where do these extra legs come from?
Here's the key insight: each rabbit has exactly 2 more legs than a chicken. So those 24 extra legs must come from rabbits! Since each rabbit contributes 2 extra legs, we divide 24 by 2 to get 12 rabbits. Then we subtract: 35 total animals minus 12 rabbits equals 23 chickens. Let's check our answer!
Now let's verify our answer is correct! We found 23 chickens and 12 rabbits. First, let's check the heads: 23 plus 12 equals 35 heads - that's right! Next, let's check the legs: 23 chickens times 2 legs each gives us 46 legs, plus 12 rabbits times 4 legs each gives us 48 legs. Adding them together: 46 plus 48 equals 94 legs - perfect! Our answer is completely correct!
Now you know the secret to solving ANY problem like this! The general method works for cars and motorcycles, spiders and beetles, or any two types of objects with different counts. Just remember: assume all are one type, calculate the expected total, find the difference, then divide by how much each item differs. For example, with 20 vehicles and 56 wheels, assume all are bikes with 2 wheels each. That gives 40 wheels, but we have 56, so 16 extra wheels. Each car has 2 more wheels than a bike, so 16 divided by 2 equals 8 cars! You're now a problem-solving expert!