This is a classic math problem called the chicken and rabbit problem. We have a cage with chickens and rabbits. We know there are 10 heads total and 26 feet total. We need to find how many chickens and how many rabbits there are.
To solve this problem, we need to set up variables. Let C represent the number of chickens and R represent the number of rabbits. We know that each chicken has 1 head and 2 feet, while each rabbit has 1 head and 4 feet. This information will help us create equations.
Now we can create our equations. Since there are 10 heads total and each animal has 1 head, we get C plus R equals 10. For the feet, chickens have 2 feet and rabbits have 4 feet, so 2C plus 4R equals 26. We now have a system of two equations with two unknowns that we can solve.
Let's solve this step by step. From the first equation, we can express C as 10 minus R. Then we substitute this into the second equation: 2 times 10 minus R plus 4R equals 26. Simplifying: 20 minus 2R plus 4R equals 26, which gives us 20 plus 2R equals 26. Solving for R: 2R equals 6, so R equals 3. Finally, C equals 10 minus 3, which equals 7.
Our final answer is 7 chickens and 3 rabbits. Let's verify this solution. For heads: 7 plus 3 equals 10, which matches our given information. For feet: 7 chickens times 2 feet each plus 3 rabbits times 4 feet each equals 14 plus 12, which equals 26 feet total. This matches perfectly! Therefore, Xiao Ming has 7 chickens and 3 rabbits in the cage.