A farm has chickens and rabbits, and there are 200 legs altogether, and 62 heads altogether. Which of these is the number of chickens?

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Let's solve this step by step. We have a farm with chickens and rabbits. We know there are 200 legs total and 62 heads total. Each chicken has 1 head and 2 legs, while each rabbit has 1 head and 4 legs. We need to find how many chickens there are. Now let's set up our variables and equations. Let C represent the number of chickens and R represent the number of rabbits. From the given information, we can write two equations. First, since each animal has one head, C plus R equals 62. Second, since chickens have 2 legs and rabbits have 4 legs, 2C plus 4R equals 200. Now let's solve this system of equations step by step. From the first equation C plus R equals 62, we can express R in terms of C. So R equals 62 minus C. Next, we substitute this expression for R into the second equation. This gives us 2C plus 4 times the quantity 62 minus C equals 200. Now let's simplify this equation step by step. We have 2C plus 4 times 62 minus C equals 200. Expanding the parentheses gives us 2C plus 248 minus 4C equals 200. Combining like terms, we get negative 2C plus 248 equals 200. Subtracting 248 from both sides gives us negative 2C equals negative 48. Finally, dividing both sides by negative 2, we find that C equals 24. Let's verify our answer. If there are 24 chickens, then there must be 62 minus 24, which equals 38 rabbits. Let's check: for heads, 24 plus 38 equals 62, which matches our given information. For legs, 24 chickens times 2 legs each gives 48 legs, plus 38 rabbits times 4 legs each gives 152 legs, for a total of 200 legs. This also matches perfectly. Therefore, the answer is 24 chickens.