please help to solve this There are 10 animals in total. They have 28 legs altogether. Some are cranes (2 legs), and some are turtles (4 legs). How many cranes and how many turtles are there?

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Let's solve this classic problem step by step. We have 10 animals total with 28 legs altogether. Some are cranes with 2 legs each, and some are turtles with 4 legs each. We need to find how many of each animal there are. First, let's define our variables. Let C represent the number of cranes and T represent the number of turtles. From the problem, we can set up two equations: C plus T equals 10 for the total number of animals, and 2C plus 4T equals 28 for the total number of legs. Now let's solve the system step by step. From the first equation, we can express C as 10 minus T. Substituting this into the second equation gives us 2 times 10 minus T plus 4T equals 28. Simplifying: 20 minus 2T plus 4T equals 28, which becomes 20 plus 2T equals 28. Therefore 2T equals 8, so T equals 4. Substituting back, C equals 6. Let's verify our solution. We found 6 cranes and 4 turtles. Checking: 6 plus 4 equals 10 animals, which is correct. For legs: 6 cranes times 2 legs each plus 4 turtles times 4 legs each equals 12 plus 16, which equals 28 legs total. Perfect! Our final answer is 6 cranes and 4 turtles. To summarize, we solved this problem using a systematic approach. First, we defined variables for the unknowns. Then we set up equations based on the given constraints. We solved the system using substitution method, and finally verified our answer. This method works for any similar two-variable linear system problem. Remember: define, set up, solve, and verify!