6-中一級英文數學題(請詳細解釋)急急急~(20點!!!)

A bag of marbles is divided evenly among some students. If each student gets 20 marbles,8 marbles are left. If each student gets 22 marbles,again 8 marbles are left. What is the minimum number of the marbles?

Let n be the number of the marbles.
The remainder is 8 when n is divided by 20. The remainder is also 8 when n is divided by 22.
Hence, n - 8 is divisible by 20 and 22.
n - 8 is a common multiple of 20 and 22.
The minimum number of the marbles is the L.C.M. of 20 and 22.
20 = 2² x 5
22 = 2 x 11
L.C.M. of 20 and 22 = 2² x 5 x 11 = 220
The minimum number of n - 8 is 220.
The minimum number of n = 220 + 8 = 228


一袋波子平均分給一些學生。若每名學生分得 20 粒波子，剩下 8 粒波子。若每名學生分得 22 粒波子，再次剩下 8 粒波子。波子的數目最小是多少？

設波子的數目為 n。
當 n 除以 20，其餘數為 8。當 n 除以 22，其餘數亦為 8。
因此，n - 8 可被 20 及 22 整除。
n - 8 是20 和 22 的公倍數。
n - 8 的最少數目是 20 和 22 的最小公倍數（L.C.M.）。
20 = 2² x 5
22 = 2 x 11
20 和 22 的 L.C.M. = 2² x 5 x 11 = 220
n - 8 的最小最目是 220。
n 的最小最目 = 220 + 8 = 228

這條題目本身是有問題的. 因為若然第一次將所有波子分給某一數目的學生後, 尚餘8粒的話, 若將相等數量的波子分給剛才的學生, 又怎可能分到每人22粒, 尚有8粒留下來呢?? 多出來的每人兩粒又從可而來呢?? 或許將題目改為將某數量波子分給兩班學生, 這樣便有可能了!!

2010-07-15 00:40:28 補充：
如果淨係計L.C.M.
the min no. of marbles is 228

L.C.M. of 20 and 22 = 220

the min no. of marbles = 220 +8 = 228

但要假設人數唔同