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78、鸡兔同䇝，共100个头， 320 只脚，那么，鸡有()只，兔有()只。

7878、鸡兔同䇝，共100100个头， 320320 只脚，那么，鸡有()只，兔有()只。

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Full solution

Q. 7878、鸡兔同䇝，共100100个头， 320320 只脚，那么，鸡有()只，兔有()只。
  1. Equations Setup: Let's denote the number of chickens as cc and the number of rabbits as rr. We know each animal has one head, so:\newlinec+r=100c + r = 100
  2. Feet Calculation: Chickens have 22 feet each and rabbits have 44 feet each. The total number of feet given is 320320, so:\newline2c+4r=3202c + 4r = 320
  3. Simplify Feet Equation: Simplify the feet equation by dividing everything by 22 to make the numbers smaller: c+2r=160c + 2r = 160
  4. Subtract Equations: Now, subtract the first equation c+r=100c + r = 100 from the simplified feet equation c+2r=160c + 2r = 160:\newlinec+2r−(c+r)=160−100c + 2r - (c + r) = 160 - 100\newliner=60r = 60
  5. Final Substitution: Substitute r=60r = 60 back into the first equation c+r=100c + r = 100:c+60=100c + 60 = 100c=40c = 40

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