Hello kids! Today we're going to learn about a fun math puzzle called the Chicken-Rabbit Problem. Imagine a farmer who has some chickens and rabbits in the same cage. He can count the heads and legs, but he wants to know exactly how many chickens and how many rabbits he has. In our example, he counts 5 heads and 14 legs total. Can you help him figure out how many of each animal there are?
Now let's understand the clues we have! Each chicken has exactly 1 head and 2 legs. Each rabbit has exactly 1 head and 4 legs. This means the total number of heads tells us how many animals there are in total. The total number of legs gives us another important clue because chickens and rabbits have different numbers of legs. By using both pieces of information together, we can solve this puzzle!
Now let's use the guessing method to solve this puzzle! First, let's try: what if all 5 animals were chickens? That would give us 5 heads, which is correct, but only 10 legs. We need 14 legs, so this doesn't work. Next, let's try: what if all 5 animals were rabbits? That gives us 5 heads, which is right, but 20 legs. That's too many! So we need a mix. Let's try 3 chickens and 2 rabbits. 3 chickens give us 6 legs, and 2 rabbits give us 8 legs. 6 plus 8 equals 14 legs! Perfect! So the answer is 3 chickens and 2 rabbits.
Now let me teach you a clever trick called the lifting legs method! Imagine all the animals lift up their front legs. After lifting, chickens would have zero legs on the ground, while rabbits would still have 2 legs on the ground. But wait, this method needs a small fix to work properly. Here's the better way: let's assume all 5 animals are chickens first. That would give us 10 legs total. But we actually have 14 legs, so we have 4 extra legs. Since each rabbit has 2 more legs than a chicken, we can find the number of rabbits by dividing: 4 divided by 2 equals 2 rabbits. And 5 minus 2 equals 3 chickens!
Now let's practice with more examples to make sure you understand! Here's Example 1: We have 8 heads and 22 legs. Let's use our method. Assume all are chickens: 8 times 2 equals 16 legs. We have 22 legs, so extra legs are 22 minus 16, which is 6. Since each rabbit has 2 more legs than a chicken, we have 6 divided by 2, which equals 3 rabbits. So we have 3 rabbits and 5 chickens. Example 2: 6 heads and 16 legs. Assume all chickens: 6 times 2 equals 12 legs. Extra legs: 16 minus 12 equals 4. Rabbits: 4 divided by 2 equals 2. So we have 2 rabbits and 4 chickens. Great job practicing!