On a farm, there are some chickens and pigs. In total, there are 35 animals. If you count all of their legs, there are a total of 100 legs. How many chickens and how many pigs are on the farm?

视频信息

答案文本 复制

视频字幕 复制

Let's solve this step by step. We have a farm with chickens and pigs. There are 35 animals total, and when we count all their legs, we get 100 legs. We need to find how many chickens and how many pigs there are. Remember, chickens have 2 legs each, and pigs have 4 legs each. Now let's set up our variables and equations. Let C represent the number of chickens and P represent the number of pigs. From the problem, we can create two equations. First, the total number of animals gives us C plus P equals 35. Second, since chickens have 2 legs and pigs have 4 legs, the total legs equation is 2C plus 4P equals 100. Now let's solve this system using the substitution method. From equation 1, we can express C in terms of P: C equals 35 minus P. Next, we substitute this expression into equation 2. So 2 times the quantity 35 minus P, plus 4P equals 100. Expanding this gives us 70 minus 2P plus 4P equals 100, which simplifies to 70 plus 2P equals 100. Now let's solve for the values. From 70 plus 2P equals 100, we subtract 70 from both sides to get 2P equals 30. Dividing by 2, we find P equals 15, so there are 15 pigs. To find the number of chickens, we substitute P equals 15 back into our first equation: C equals 35 minus 15, which gives us C equals 20. Therefore, there are 20 chickens and 15 pigs on the farm. Let's verify our answer to make sure it's correct. First, we check the total number of animals: 20 chickens plus 15 pigs equals 35 animals, which matches our given information. Next, we check the total legs: 20 chickens times 2 legs each gives 40 legs, plus 15 pigs times 4 legs each gives 60 legs, for a total of 100 legs. This also matches perfectly. Therefore, our final answer is confirmed: there are 20 chickens and 15 pigs on the farm.