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HELP ME....MaTH...PLEASE...
發問:
問題如下: Find the least number which,when divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45. I think like this: X/35=Y...25 X/45=Y...35 X/55=Y...45 What is X???????????
計呢種數有種叫韓信點兵法~ Find the least number which,when divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45. step 1: 搵45, 55 既公倍數, 同時呢個數除35 時余25 經過trial and error, we find 2475, 2475 = 35 x A + 25 = 45 x 55 x B where A B are integers. step 2: 搵35, 55 既公倍數, 同時呢個數除45 時余35 經過trial and error, we find 1925, 1925 = 45 x C + 35 = 35 x 55 x D where C D are integers step 3: 搵35, 45 既公倍數, 同時呢個數除55 時余45 經過trial and error, we find 2520, 2520 = 55 x E + 45 = 35 x 45 x F where E F are integers step 4: add up all these no. 2475 + 1925 + 2520 = (35 x A + 25) + (35 x 55 x D) + (35 x 45 x F) ----------------------- = 25 + 35 (A +55D + 45F) ---------also---------- = (45 x C + 35) + (45 x 55 x B) + (35 x 45 x F ) ------------------------= 35 + 45 (C +55B + 35F) ---------also-----------= (55 x E + 45) + (45 x 55 x B) + (35 x 55 x D) ------------------------= 45 + 55 (E + 45B + 35D ) ------------------------= 6920 由上可見, 這6920 divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45.但太大了~ step 5 : 6920 - n(L.C.M of 35, 45, 55) 6920 - n3465 > 0 n = 1 least value thus 6420 - 3465 = 2955 2008-09-03 22:10:08 補充： 可能step4 亂d, 有唔明閣下可以補充, 我會盡力解答~
其他解答:
HELP ME....MaTH...PLEASE...
發問:
問題如下: Find the least number which,when divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45. I think like this: X/35=Y...25 X/45=Y...35 X/55=Y...45 What is X???????????
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最佳解答:計呢種數有種叫韓信點兵法~ Find the least number which,when divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45. step 1: 搵45, 55 既公倍數, 同時呢個數除35 時余25 經過trial and error, we find 2475, 2475 = 35 x A + 25 = 45 x 55 x B where A B are integers. step 2: 搵35, 55 既公倍數, 同時呢個數除45 時余35 經過trial and error, we find 1925, 1925 = 45 x C + 35 = 35 x 55 x D where C D are integers step 3: 搵35, 45 既公倍數, 同時呢個數除55 時余45 經過trial and error, we find 2520, 2520 = 55 x E + 45 = 35 x 45 x F where E F are integers step 4: add up all these no. 2475 + 1925 + 2520 = (35 x A + 25) + (35 x 55 x D) + (35 x 45 x F) ----------------------- = 25 + 35 (A +55D + 45F) ---------also---------- = (45 x C + 35) + (45 x 55 x B) + (35 x 45 x F ) ------------------------= 35 + 45 (C +55B + 35F) ---------also-----------= (55 x E + 45) + (45 x 55 x B) + (35 x 55 x D) ------------------------= 45 + 55 (E + 45B + 35D ) ------------------------= 6920 由上可見, 這6920 divided by 35,leaves a remainder 25, when divided by 45 leaves 35,when divided by 55 leaves 45.但太大了~ step 5 : 6920 - n(L.C.M of 35, 45, 55) 6920 - n3465 > 0 n = 1 least value thus 6420 - 3465 = 2955 2008-09-03 22:10:08 補充： 可能step4 亂d, 有唔明閣下可以補充, 我會盡力解答~
其他解答:
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