设

1头牛1周吃草量 —— X

草场1周长草量 —— Y

草场原有草量 —— N

则

27*6 X = 6Y + N ====> 162X = 6Y + N

23*9 X = 9Y + N ====> 207X = 9Y + N

两式相减得到 45X = 3Y ====> Y = 15X

代入，得到 162X = 90X + N =====> N = 72X


设

21头牛需要Z周吃完

则

21*Z*X = Z*Y + N

代入，得到 21X*Z = 15X*Z + 72X =====> 6X*Z = 72X ====> Z = 12